CoCalc -- trans12.grp

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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
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#############################################################################
##
#W  trans12.grp         GAP transitive groups library        Alexander Hulpke
##
##
#Y  Copyright (C)  1997,  Lehrstuhl D für Mathematik,  RWTH Aachen,  Germany
##
##  This file contains the transitive groups of degree 12
##  They were originally published by Gordon Royle
##


TRANSGRP[12]:=
[[(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"C(4)[x]C(3)"],
[(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"E(4)[x]C(3)=6x2"],
[(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,11)(2,8)(3,9)(4,6)(5,7)(10,12),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"D_6(6)[x]2=1/2[3:2]E(4)"],
[(1,9,5)(2,4,3)(6,8,7)(10,12,11),(1,11,6)(2,9,7)(3,10,5)(4,8,12),
"A_4(12)"],
[(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
(1,8,7,2)(3,6,9,12)(4,11,10,5),"1/2[3:2]4"],
[(1,9,5)(2,4,3)(6,8,7)(10,12,11),(1,11,6)(2,9,7)(3,10,5)(4,8,12),
(1,7)(2,11)(3,12)(4,10)(5,8)(6,9),"A_4(12)x2"],
[(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"A_4(6)[x]2=[1/8.2^6]3"],
[(1,2)(3,5)(4,6)(7,9)(8,10),(1,3,6,12)(2,4,7,10)(5,8,11,9),"S_4(12d)"],
[(1,7)(3,9)(4,10)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,2)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2[1/8.2^6]S(3)=S_4(12e)"],
[(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
"S(3)[x]E(4)"],
[(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,4,7,10)(2,5,8,11)(3,6,9,12),"S(3)[x]C(4)"],
[(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,11)(2,10)(3,9)(4,8)(5,7),"1/2[3:2]cD(4)"],
[(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),(1,11)(2,10)(3,9)(4,8)(5,7),
"1/2[3:2]eD(4)"],[(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,7)(3,9)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"D(4)[x]C(3)"],
[(1,5,9)(2,6,10)(3,7,11)(4,8,12),(2,8)(4,10)(6,12),(1,7)(3,9)(5,11),
(1,2)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2[3:2]dD(4)"],
[(2,10,6)(4,8,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[3^2]E(4)"],
[(2,10,6)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),"[3^2]4"],
[(2,6,10)(4,8,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[3^2]E(4)"],
[(2,6,10)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),"[3^2]4"],
[(2,8,11)(3,6,12)(4,7,10),(1,7,10)(2,5,11)(3,6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"A(4)[x]C(3)"],
[(3,9)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,2)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2[1/4.2^6]S(3)"],
[(1,2)(3,5)(4,6)(7,9)(8,10),(1,3,6,12)(2,4,7,10)(5,8,11,9),
(1,9)(2,7)(3,5)(4,10)(6,8)(11,12),"S_4(12d)x2"],
[(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(2,10)(3,11)(4,8)(5,9),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
"S_4(6d)[x]2=[1/8.2^6]S(3)"],
[(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,7)(2,10)(3,11)(4,8)(5,9)(6,12),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
"S_4(6c)[x]2"],
[(1,7)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,12)(2,3)(4,5)(6,7)
(8,9)(10,11),"2A_4(6)[x]2=[1/4.2^6]3"],
[(1,9,5)(2,4,3)(6,8,7)(10,12,11),(1,11,6)(2,9,7)(3,10,5)(4,8,12),
(1,7)(2,11)(3,12)(4,10)(5,8)(6,9),(1,4)(2,5)(3,9)(6,12)(7,10)(8,11),
"A_4(12)x2^2"],
[(1,7)(2,11)(3,12)(4,10)(5,8)(6,9),(1,9,5)(2,4,3)(6,8,7)(10,12,11),
(1,11,6)(2,9,7)(3,10,5)(4,8,12),(1,4,7,10)(2,3,11,12)(5,6,8,9),
"[2]S_4(6)_2"],[(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,7)(3,9)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),"D(4)[x]S(3)"],
[(1,7)(3,9)(4,10)(6,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[1/2.4^2]3"],
[(3,9)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,8,7,2)(3,6,9,12)(4,11,10,5),"1/2[1/4.4^3]S(3)"],
[(1,10,7,4)(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[4^2]3"],
[(1,10)(3,12)(4,7)(6,9),(1,7)(3,9)(4,10)(6,12),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[E(4)^2]3"],
[(1,3,5,7,9)(2,4,6,8,12),(1,11,5)(2,7,9)(3,6,8)(4,12,10),"A_5(12)"],
[(1,3,5,7,9,11)(2,4,6,8,10,12),(1,8)(2,3)(4,5)(6,7)(9,12)(10,11),
"F_36:2(12e)"],
[(2,6,10)(4,8,12),(2,8)(4,6)(10,12),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
"[D_6^2]2=D_6wr2"],
[(1,3,5,7,9,11)(2,4,6,8,10,12),(1,9)(2,3)(6,7)(8,12)(10,11),"F_36:2(12d)"
],
[(2,6,10)(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,10)(2,5)(3,12)(4,7)(6,9)
(8,11),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[3^2:2]E(4)"],
[(2,6,10)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,11)(2,10)(3,9)(4,8)(5,7),"1/2[3^2:2]cD(4)"],
[(2,6,10)(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12)
,"[3^2:2]4"],
[(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),(1,7)(2,8,10,4)(3,9,11,5)
(6,12),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"F_36(6)[x]2"],
[(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),(1,5,9)(4,8,12),
(2,10)(3,11)(4,8)(5,9),(1,6,12,7)(2,8,11,5)(3,9,10,4),
"1/2[(1/4.2^3)^2]F_36(6)"],
[(2,6,10)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,7)(3,9)(5,11),
"[3^2]D(4)=6wr2"],
[(2,8,11)(3,6,12)(4,7,10),(1,7,10)(2,5,11)(3,6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),"A(4)[x]S(3)"],
[(1,5,9)(2,6,10)(3,7,11)(4,8,12),(2,8,11)(3,6,12)(4,7,10),
(1,7,10)(2,5,11)(3,6,9),(1,11)(2,10)(3,9)(4,8)(5,7),"1/2[3:2]S(4)"],
[(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,10)(2,5)(6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"S(4)[x]C(3)"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,4,2,11,5,8,10,7)(3,9,12,6),"[(1/3.3^3):2]4_4"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,2,5,10)(3,12)(4,11,8,7)(6,9),(1,4,5,8)(2,7,10,11)(3,6)(9,12),
"[(1/3.3^3):2]E(4)_4"],
[(1,7)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"2S_4(6)[x]2=[1/4.2^6]S(3)"],
[(1,9)(2,7)(3,5)(4,10)(6,8)(11,12),(1,2)(3,5)(4,6)(7,9)(8,10),
(1,3,6,12)(2,4,7,10)(5,8,11,9),(1,2,9,7)(3,11,5,12)(4,8,10,6),
"[2]2S_4(6)_2"],
[(3,9)(6,12),(1,7)(3,9)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,2)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2e[1/16.D(4)^3]S(3)"],
[(3,9)(6,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),(1,7)(3,9)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[1/16.D(4)^3]3"],
[(3,9)(6,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,11)(2,10)(3,9)(4,8)(5,7),
"1/2c[1/16.D(4)^3]S(3)"],
[(1,7)(3,9)(4,10)(6,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),"[1/2.4^2]S(3)"]
,
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(2,3)(4,9)(5,8)(6,10)(7,
11),(1,2)(3,12)(4,11)(5,10)(6,9)(7,8),"[(1/2.2^2)^3]D(6)_4"],
[(3,9)(6,12),(1,10,7,4)(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"[1/2.4^3]3"],
[(3,9)(6,12),(1,10)(3,12)(4,7)(6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"[1/2.2^6]3"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,2,12,3)(4,7)(5,6)
(8,9),"[(1/2.2^2)^3]A_4(6)_4"],
[(1,12)(4,5),(1,12)(8,9),(1,3,5,7,9,11)(2,4,6,8,10,12),"[2^4]6"],
[(1,12)(2,3)(6,7)(8,9),(1,12)(2,3)(4,5),(2,8)(3,9)(4,10)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[2^3]A_4(6)"],
[(1,12)(2,3)(6,7)(8,9),(1,3,5,7,9,11)(2,4,6,8,10,12),
(4,10)(5,11)(6,7)(8,9),"[1/2[1/2.2^2]^3]2A_4(6)_4"],
[(1,12)(2,3)(6,7)(8,9),(1,12)(2,3)(4,5),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(2,8)(3,9)(4,11)(5,10)(6,7),
"[2^3]A_4(6)_4"],
[(1,10,7,4)(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[4^2]S(3)"],
[(1,12)(2,3)(6,7)(8,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,2)(3,12)(4,5)(6,8)(7,9)(10,11),"[1/2[1/2.2^2]^3]S_4(6d)_8b"],
[(1,12)(2,3)(6,7)(8,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,2)(3,12)(4,5)(6,9)(7,8),"[1/2[1/2.2^2]^3]S_4(6d)_8a"],
[(1,12)(2,3)(6,7)(8,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,3)(2,12)(4,10)(5,11)(6,8)(7,9),(1,5)(2,9)(3,8)(4,12)(6,11)(7,10),
"[1/2[1/2.2^2]^3]S_4(6c)_4"],
[(1,12)(2,3)(6,7)(8,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,3,5)(2,4,12)(6,8,10)(7,9,11),(2,4)(3,5)(6,7)(8,11)(9,10),
"[1/2[1/2.2^2]^3]S_4(6d)_2"],
[(1,10)(3,12)(4,7)(6,9),(1,7)(3,9)(4,10)(6,12),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),"[E(4)^2]S(3)"],
[(1,12)(2,3)(6,7)(8,9),(2,8)(3,9)(4,10)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,7)(2,10)(3,11)(4,8)(5,9)(6,12),
"[1/2[1/2.2^2]^3]S_4(6c)"],
[(1,12)(4,5),(1,12)(8,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,11)(2,8)(3,9)(4,6)(5,7)(10,12),"[2^4]D_6(6)"],
[(2,6,10)(3,7,11)(4,8,12),(1,2)(3,12)(4,11)(5,10)(6,9)(7,8),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"1/2[3^3:2]E(4)"],
[(2,6,10)(3,7,11)(4,8,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[3^3]E(4)"],
[(2,6,10)(3,7,11)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),"[3^3]4"],
[(2,6,10)(3,7,11)(4,8,12),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
(1,8,7,2)(3,6,9,12)(4,11,10,5),"1/2[3^3:2]4"],
[(2,4,6,8,10)(3,5,7,9,11),(1,10)(2,7)(3,12)(4,5)(6,11)(8,9),"S_5(12)"],
[(1,3,5,7,9)(2,4,6,8,12),(1,11)(2,8)(3,9)(10,12),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"L(6)[x]2"],
[(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),(2,4,6,8,10)(3,5,7,9,11),
(4,10)(5,11)(6,8)(7,9),(1,2)(3,12)(4,11)(5,10),"[2]L(6)_6"],
[(2,6,10)(4,8,12),(2,10)(4,8),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[S(3)^2]E(4)"],
[(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),(1,3,5,7,9,11)(2,4,6,8,10,12),
(1,3,5,11,9,7)(2,4,10,8,6,12),(2,3)(6,11)(7,10),"[2]F_36:2_2{S_3^2}"],
[(2,6,10)(4,8,12),(2,10)(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),"[S(3)^2]4"
],[(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),(2,6,10)(3,7,11),
(1,3)(2,12)(4,6,8,10)(5,7,9,11),(2,3)(6,11)(7,10),"[2]F_36:2_2{3^2:4}"],
[(2,6,10)(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12)
,(1,7)(3,9)(5,11),"[3^2:2]D(4)"],
[(1,12)(4,5)(8,9),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,7)(2,8,10,4)(3,9,11,5)(6,12),"[(1/4.2^3)^2]F_36(6)"],
[(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,10)(2,5)(6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),"S(4)[x]S(3)"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,4,2,11,5,8,10,7)(3,9,12,6),(3,4)(6,10)(7,12)(8,11),
"[(1/3.3^3):2]D(4)_4"],[(1,10)(3,12)(4,7)(6,9),(1,7,10)(2,5,11)(3,6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[1/4E(4)^3:3]3"],
[(3,9)(6,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),(1,7)(3,9)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
"[1/16.D(4)^3]S(3)"],
[(1,12)(2,3),(1,3,5,7,9,11)(2,4,6,8,10,12),"[2^5]6"],
[(1,12)(6,7),(1,12)(2,3)(4,5),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,3,11)(2,10,12)(4,6,8)(5,7,9),"[2^4]A_4(6)"],
[(1,12)(2,3),(1,7,9,3,5,11)(2,4,10,12,6,8),(1,12)(4,6)(5,7)(10,11),
"[(1/2.2^2)^3]2A_4(6)_4{n4}"],
[(3,12)(6,9),(3,9)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"[E(4)^3]3=E(4)wr3"],
[(1,12)(2,3),(1,7,9,3,5,11)(2,4,10,12,6,8),(6,7)(8,10,9,11),
"[(1/2.2^2)^3]2A_4(6)_4{n2}"],
[(1,12)(6,7),(1,12)(2,3)(4,5),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(2,8)(3,9)(4,10)(5,11)(6,7),"[2^4]A_4(6)_4{n4}"],
[(1,12)(6,7),(1,12)(2,3)(4,5),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(2,8,3,9)(4,10)(5,11),"[2^4]A_4(6)_4{n2}"],
[(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[4^3]3=4wr3"],
[(3,9)(6,12),(1,10,7,4)(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[1/2.4^3]S(3)"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(2,3)(4,10)(5,11)(6,8)(7,9),"[(1/2.2^2)^3]S_4(6d)_8"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,3)(2,12)(4,8)(5,9)(6,11)(7,10),"[(1/2.2^2)^3]S_4(6c)_4"],
[(3,9)(6,12),(1,10,7,4)(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,8,7,2)(3,6,9,12)(4,11,10,5),"1/2[4^3]S(3)"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(4,6)(5,7)(8,10)(9,11),
(2,3)(4,5)(8,10,9,11),"[(1/2.2^2)^3]2A_4(6)_2"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,7,11)(2,4,8)(3,5,9)(6,10,12),(2,3)(4,8)(5,9)(6,11)(7,10),
"[(1/2.2^2)^3]S_4(6d)_2"],
[(3,9)(6,12),(1,10)(3,12)(4,7)(6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[1/2.2^6]S(3)"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,7,11)(2,4,8)(3,5,9)(6,10,12),(1,2,12,3)(4,8,5,9)(6,11,7,10),
"[(1/2.2^2)^3]S_4(6c)_2"],
[(3,12)(6,9),(1,7)(3,9)(4,10)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,11)(2,4)(3,9)(5,7)(6,12)(8,10),"1/2[E(4)^3]S(3)"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(6,7)(8,10)(9,11),
"[(1/2.2^2)^3]2A_4(6)_8"],
[(1,12)(2,3),(1,2,4,6,8,10,12,3,5,7,9,11),"1/2[2^6]6"],
[(1,12)(2,3),(1,12)(4,5),(1,12)(6,7),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,11)(2,8)(3,9)(4,6)(5,7)(10,12),"[2^5]D_6(6)"],
[(1,12)(2,3),(1,12)(4,5),(1,12)(6,7),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,10,12,11)(2,8)(3,9)(4,6)(5,7),"1/2[2^6]D_6"],
[(1,12)(4,5),(1,12)(8,9),(1,3,5,7,9,11)(2,4,6,8,10,12),
(1,10,12,11)(2,9,3,8)(4,6)(5,7),"1/2[2^5]D(6)"],
[(1,12)(4,5),(1,12)(8,9),(1,3,5,7,9,11)(2,4,6,8,10,12),
(1,11)(2,8)(3,9)(4,6)(5,7)(10,12),"[2^4]D(6)"],
[(1,12)(2,3)(6,7)(8,9),(1,12)(2,3)(4,5),(2,8)(3,9)(4,10)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(2,10)(3,11)(4,8)(5,9),"[2^3]S_4(6d)"],
[(1,12)(2,3)(6,7)(8,9),(1,12)(2,3)(4,5),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,3,11)(2,10,12)(4,6,8)(5,7,9),
(2,4)(3,5)(6,7)(8,11)(9,10),"[2^3]S_4(6)_2"],
[(1,12)(2,3)(6,7)(8,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,3)(2,12)(4,10)(5,11)(6,8)(7,9),(2,3)(4,10)(5,11)(6,7),
"[1/2[1/2.2^2]^3]2S_4(6)_8"],
[(1,12)(2,3)(6,7)(8,9),(1,3,5,7,9,11)(2,4,6,8,10,12),
(1,3)(2,12)(4,10)(5,11)(6,8)(7,9),(4,10)(5,11)(6,7)(8,9),
"[1/2[1/2.2^2]^3]2S_4(6)_4"],
[(1,12)(2,3)(6,7)(8,9),(1,12)(2,3)(4,5),(1,5,9)(2,6,10)(3,7,11)
(4,8,12),(2,10)(3,11)(4,8)(5,9),(2,4)(3,5)(8,11)(9,10),
"[2^3]S_4(6)_4"],
[(1,12)(2,3)(6,7)(8,9),(1,12)(2,3)(4,5),(1,5,9)(2,6,10)(3,7,11)
(4,8,12),(2,4)(3,5)(6,7)(8,10)(9,11),"[2^3]S_4(6)_8"],
[(2,6,10)(3,7,11)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,7)(3,9)(5,11),"[3^3]D(4)"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
"[3^3:2]E(4)"],
[(2,6,10)(3,7,11)(4,8,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),(1,11)(2,10)(3,9)(4,8)(5,7),
"1/2[3^3:2]eD(4)"],[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,4,7,10)(2,5,8,11)(3,6,9,12),"[3^3:2]4"],
[(2,6,10)(3,7,11)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,11)(2,10)(3,9)(4,8)(5,7),"1/2[3^3:2]cD(4)"],
[(2,6,10)(3,7,11)(4,8,12),(2,8)(4,10)(6,12),(1,7)(3,9)(5,11),
(1,2)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2[3^3:2]dD(4)"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(2,3,4)(6,7,8)(10,11,12),(1,7,2)(3,6,9)(5,11,10),"[(1/3.3^3):2]A(4)_4"],
[(1,3,5,7,9)(2,4,6,8,12),(1,11)(2,4)(3,5)(6,8)(7,9)(10,12),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"L(6):2[x]2"],
[(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),(2,4,6,8,10)(3,5,7,9,11),
(1,3,12,2)(4,6,5,7)(8,11,9,10),"[2]L(6):2_12"],
[(2,6,10)(4,8,12),(2,10)(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,7)(3,9)(5,11),"[S(3)^2]D(4)=D(6)wr2"],
[(2,8)(4,10),(2,6,10)(4,8,12),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
"[A_4^2]2=A_4wr2"],[(1,10)(3,12)(4,7)(6,9),(1,7,10)(2,5,11)(3,6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,2)(4,8)(5,10)(6,9)(7,11),
"[1/4E(4)^3:3]S(3)_2"],[(1,10)(3,12)(4,7)(6,9),(1,7,10)(2,5,11)(3,6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
"[1/4E(4)^3:3]S(3)"],[(1,10)(3,12)(4,7)(6,9),(1,7,10)(2,5,11)(3,6,9),
(4,7)(6,9)(8,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[1/4E(4)^3:3:2]3"],
[(4,8,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),(1,7)(2,8)(3,9)(4,10)(5,11)
(6,12),"[3^4]E(4)=3wrE(4)"],
[(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),"[3^4]4=3wr4"],
[(2,6,10)(3,7,11)(4,8,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),(1,7,10)(2,5,11)(3,6,9)(4,8,12),
"1/3[3^4]A(4)"],[(2,6,10)(3,7,11)(4,8,12),(2,8,11)(3,6,12)(4,7,10),
(1,7,10)(2,5,11)(3,6,9),"[3^3]A(4)"],
[(1,12),(1,3,5,7,9,11)(2,4,6,8,10,12),"[2^6]6=2wr6"],
[(1,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,11)(2,8)(3,9)(4,6)(5,7)
(10,12),"[2^6]D_6=2wrD_6(6)"],
[(1,12)(2,3),(1,3,5,7,9,11)(2,4,6,8,10,12),(1,11)(2,8)(3,9)(4,6)(5,7)
(10,12),"[2^5]D(6)"],
[(1,12)(6,7),(1,12)(2,3)(4,5),(2,8)(3,9)(4,10)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(2,10)(3,11)(4,8)(5,9),"[2^4]S_4(6d)"],
[(1,12)(2,3),(1,11,5,3,9,7)(2,8,6,12,10,4),(4,8)(5,9)(6,10)(7,11),
(4,10)(5,11)(6,9)(7,8),"[(1/2.2^2)^3]2S_4(6)_4"],
[(3,12)(6,9),(3,9)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[E(4)^3]S(3)=E(4)wrS(3)"],
[(1,12)(6,7),(1,12)(2,3)(4,5),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(2,10)(3,11)(4,8)(5,9),(2,4)(3,5)(8,11)(9,10),"[2^4]S_4(6d)_4"],
[(3,6,9,12),(1,7)(3,9)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"[1/4.cD(4)^3]3"],
[(3,12)(6,9),(3,9)(6,12),(1,7)(3,9)(5,11),(1,5,9)(2,6,10)(3,7,11)
(4,8,12),"[1/4.eD(4)^3]3"],
[(1,12)(6,7),(1,12)(2,3)(4,5),(1,3,5,7,9,11)(2,4,6,8,10,12),
(4,10)(5,11)(6,7),"[2^4]2A_4(6)_4"],
[(1,12)(2,3),(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"[2^5]A_4(6)"],
[(1,12)(2,3),(1,3,5,7,9,11)(2,4,6,8,10,12),(1,10,12,11)(2,8)(3,9)(4,6)
(5,7),"1/2[2^6]D(6)"],
[(1,12)(6,7),(1,12)(2,3)(4,5),(2,8)(3,9)(4,10)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,7)(2,10)(3,11)(4,8)(5,9)(6,12),
"[2^4]S_4(6c)"],
[(1,12)(2,3),(1,11,5,3,9,7)(2,8,6,12,10,4),(2,3)(4,10)(5,11)(6,8)(7,9)
,"[(1/2.2^2)^3]2S_4(6)_8"],
[(3,12)(6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,11)(2,10)(3,9)(4,8)(5,7),"1/2[1/4.eD(4)^3]S(3)"],
[(1,12)(6,7),(1,12)(2,3)(4,5),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,3)(2,12)(4,10)(5,11)(6,8)(7,9),(2,8)(3,9)(4,10)(5,11)(6,7),
"[2^4]S_4(6c)_4"],
[(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
"[4^3]S(3)=4wrS(3)"],
[(3,6,9,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,11)(2,10)(3,9)(4,8)
(5,7),"1/2[1/4.cD(4)^3]S(3)"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(4,8,6,10)(5,9,7,11),
(2,3)(4,8)(5,9)(6,11)(7,10),"[(1/2.2^2)^3]2S_4(6)_2{S_4(6c)}"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,3)(2,12)(4,8,6,10)(5,9,7,11),(1,2,12,3)(4,6,5,7)(8,10,9,11),
"[(1/2.2^2)^3]2S_4(6)_2{S_4(6d)}"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,3)(2,12)(4,10)(5,11)(6,8)(7,9),(2,3)(4,8)(5,9)(6,10)(7,11),
"[2^5]D(6)_2t"],
[(1,12)(2,3),(1,5,9)(2,6,10)(3,7,11)(4,8,12),(4,8)(5,9)(6,10)(7,11),
(1,2,12,3)(4,10,5,11)(6,8,7,9),"[2^5]D(6)_2i"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,7)(3,9)(5,11),"[3^3:2]D(4)"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,4,2,11,5,8,10,7)(3,9,12,6),(2,3,4)(6,7,8)(10,11,12),
"[(1/3.3^3):2]S(4)_4"],
[(1,12)(2,3),(1,5,9)(4,8,12),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
"[2^5]F_18(6)"],
[(1,12)(2,3),(1,5,9)(4,8,12),(2,6,10)(3,7,11),(1,2,12,3)(4,10,5,11)
(6,8,7,9),"[2^5]F_18(6)_2"],
[(2,8)(4,10),(2,6,10)(4,8,12),(1,7)(2,10)(3,11)(4,8)(5,9)(6,12),
(1,12,7,6)(2,11,10,3)(4,9,8,5),"1/2[S_4(6c)^2]2"],
[(2,8)(4,10),(2,6,10)(4,8,12),(1,7)(2,10)(3,11)(4,8)(5,9)(6,12),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"[1/2.S_4(6c)^2]2"],
[(1,12)(4,5),(1,12)(8,9),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,7)(2,8,10,4)(3,9,11,5)(6,12),"[2^4]F_36(6)"],
[(1,12)(4,5),(1,12)(8,9),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[2^4]F_18(6):2"],
[(3,12)(6,9),(3,9)(6,12),(2,8,11)(3,6,12)(4,7,10),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[1/9.A(4)^3]3"],
[(1,10)(3,12)(4,7)(6,9),(1,7,10)(2,5,11)(3,6,9),(4,7)(6,9)(8,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
"[1/4E(4)^3:3:2]3"],[(3,12)(6,9),(3,9)(6,12),(2,8,11)(3,6,12)(4,7,10),
(1,3,11,7,6,2,10,9,5)(4,12,8),"[1/9.A(4)^3]3_3"],
[(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,7)(3,9)(5,11),
"[3^4]D(4)=3wrD(4)"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[3^4:2]E(4)"],
[(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,11)(2,10)(3,9)(4,8)(5,7),
"1/2[3^4:2]cD(4)"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12),
"[3^4:2]4"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7,5,11)(2,8,10,4)(3,9)(6,12),"[3^4:2]E(4)_2"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,4)(3,9)(5,11)(6,12)(8,10),"1/2[3^4:2^2]E(4)"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,4,7,10,5,8,11,2)(3,6,9,12),
"[3^4:2]4_4"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,10,5,2)(3,12)(4,7,8,11)(6,9),
(1,7,5,11)(2,8,10,4)(3,9)(6,12),"[3^4:2]E(4)_4"],
[(2,6,10)(3,7,11)(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,10)(2,5)(6,9),"[3^3]S(4)"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(2,8,11)(3,6,12)(4,7,10),(1,7,10)(2,5,11)(3,6,9),"[3^3:2]A(4)"],
[(2,6,10)(3,7,11)(4,8,12),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(3,8)(4,7)(5,9)(6,10)(11,12),(2,7)(3,6)(4,8)(5,9)(10,11),"[3^3]S(4)_6"]
,[(2,6,10)(3,7,11)(4,8,12),(2,8,11)(3,6,12)(4,7,10),
(1,7,10)(2,5,11)(3,6,9),(1,11)(2,10)(3,9)(4,8)(5,7),"1/2[3^3:2]S(4)"],
[(1,2,3,4,5,6,7,8,9,10,12),(1,10)(2,5)(3,7)(4,8)(6,9)(11,12),"L(2,11)"]
,
[(1,3,5)(2,4,12),(2,4,6,8,10)(3,5,7,9,11),(1,12)(2,3)(4,5)(6,7)(8,9)
(10,11),"A(6)[x]2"],
[(1,3,5)(2,4,12)(7,9,11),(1,7,3,9,5)(2,4,6,8,10),
(1,12)(2,3,4,5)(6,11,8,9)(7,10),"M_10(12)=[A_6[1/360]{M_10}A_6]2_2"],
[(1,3,5)(2,4,12)(7,9,11),(1,7,3,9,5)(2,4,6,8,10),
(1,12)(2,3)(4,11)(5,10)(6,9)(7,8),"PGL(2,9)(12)=[A_6[1/360]{M_10}A_6]2"],
[(1,3,5)(2,4,12),(2,4,6,8,10)(3,5,7,9,11),(1,12)(2,3)(4,5)(6,7)(8,11)
(9,10),"S_6(12)"],
[(1,12)(2,3),(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(2,10)(3,11)(4,8)(5,9),"[2^5]S_4(6d)"],
[(3,6,9,12),(1,7)(3,9)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[1/4.cD(4)^3]S(3)"],
[(3,12)(6,9),(3,9)(6,12),(1,7)(3,9)(5,11),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
"[1/4.eD(4)^3]S(3)"],
[(1,12)(2,3),(1,7)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[2^5]2A_4(6)"],
[(1,12),(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"[2^6]A_4=2wrA_4(6)"],
[(3,6,9,12),(1,7)(3,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[1/2.cD(4)^3]3"],
[(1,12)(2,3),(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,12)(2,10)(3,11)(4,8)(5,9),"1/2[2^6]S_4(6d)"],
[(1,12)(2,3),(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,7)(2,10)(3,11)(4,8)(5,9)(6,12),"[2^5]S_4(6c)"],
[(1,12)(2,3),(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,6,12,7)(2,10)(3,11)(4,8)(5,9),"1/2[2^6]S_4(6c)"],
[(1,12),(1,3,5,7,9,11)(2,4,6,8,10,12),(1,11)(2,8)(3,9)(4,6)(5,7)(10,12)
,"[2^6]D(6)=2wrD(6)"],
[(4,8,12),(2,8,11)(3,6,12)(4,7,10),(1,7,10)(2,5,11)(3,6,9),
"[3^4]A(4)=3wrA(4)"],
[(1,12)(2,3),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[2^5]F_18(6):2"],
[(1,12)(2,3),(1,5,9)(4,8,12),(1,3,5,7,9,11)(2,4,6,8,10,12),
(2,3)(4,8)(5,9)(6,10)(7,11),"[2^5]F_18:2_2"],
[(1,12)(2,3),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,6,12,7)(2,8)(3,9)(4,10)(5,11),"1/2[2^6]F_18:2"],
[(1,12)(2,3),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,6,12,7)(2,8,10,4)(3,9,11,5),"1/2[2^6]F_36"],
[(1,12)(2,3),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,7)(2,8,10,4)(3,9,11,5)(6,12),"[2^5]F_36(6)"],
[(2,8)(4,10),(2,6,10)(4,8,12),(2,10)(4,8)(6,12),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"[S_4(6c)^2]2=S_4(6c)wr2"],
[(1,12)(4,5),(1,12)(8,9),(1,3,5,11,9,7)(2,4,10,8,6,12),
(2,6,10)(3,7,11),(6,10)(7,11)(8,9),"[2^4]F_36:2_4"],
[(1,12)(4,5),(1,12)(8,9),(1,3,5,11,9,7)(2,4,10,8,6,12),
(2,6,10)(3,7,11),(2,6)(3,7)(4,8)(5,9),(2,3)(6,10)(7,11)(8,9),
"[2^4]F_36:2_2"],
[(2,8)(4,10),(2,6,10)(4,8,12),(2,10)(4,8),(1,12)(2,3)(4,5)(6,7)(8,9)
(10,11),"[S_4(6d)^2]2=S_4(6d)wr2"],
[(3,12)(6,9),(3,9)(6,12),(2,8,11)(3,6,12)(4,7,10),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,2)(4,8)(5,10)(6,9)(7,11),
"[1/9.A(4)^3]S(3)_2"],
[(3,12)(6,9),(3,9)(6,12),(2,8,11)(3,6,12)(4,7,10),(1,10)(2,5)(6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[E(4)^3:3:2]3"],
[(3,12)(6,9),(3,9)(6,12),(2,8,11)(3,6,12)(4,7,10),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
"[1/9.A(4)^3]S(3)"],[(3,12)(6,9),(3,9)(6,12),(2,8,11)(3,6,12)(4,7,10),
(1,2)(4,11)(5,7)(6,9)(8,10),(1,3)(4,12)(6,10)(7,9)(8,11),
"[1/9.A(4)^3]S(3)_6"],
[(6,12),(2,6,10)(4,8,12),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
"[2A_4^2]2=2A4wr2=2wrF_18(6)"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,7)(2,10)(3,9)(4,8)(5,11),"1/2[3^4:2^2]cD(4)"],
[(4,8,12),(2,10)(4,8),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[3^4:2^2]E(4)"],
[(4,8,12),(2,10)(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),"[3^4:2^2]4"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,2,5,10)(3,12)(4,7,8,11)(6,9),
(2,3)(5,9)(6,11)(7,10),"[3^4:2]D(4)_8"],
[(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,10)(2,5)(6,9),"[3^3:2]S(4)"],
[(4,8,12),(2,10)(4,8),(1,7)(2,8,10,4)(3,9,11,5)(6,12),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"[1/2.F_36^2]2"],
[(4,8,12),(2,10)(4,8),(1,7)(2,8,10,4)(3,9,11,5)(6,12),
(1,12,7,6)(2,9,8,11,10,5,4,3),"1/2[F_36^2]2"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
(2,3)(5,9)(6,11)(7,10),"[3^4:2]D(4)_4"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,7)(3,9)(5,11),"[3^4:2]D(4)"],
[(1,2,3,4,5,6,7,8,9,10,12),(1,10)(2,5)(3,7)(4,8)(6,9)(11,12),
(1,2,4,8,5,10,9,7,3,6),"PGL(2,11)"],
[(1,3)(2,12),(1,3,5,7,9,11)(2,4,6,8,10,12),(1,12)(2,3)(4,5)(6,7)(8,9)
(10,11),"S(6)[x]2"],
[(1,3,5)(2,4,12)(7,9,11),(1,7,3,9,5)(2,4,6,8,10),
(1,9)(2,12)(3,7)(5,11),(1,12)(2,3)(4,11)(5,10)(6,9)(7,8),
"M_10.2(12)=A_6.E_4(12)=[S_6[1/720]{M_10}S_6]2"],
[(3,6,9,12),(1,7)(3,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[1/2.cD(4)^3]S(3)"],
[(3,6,9,12),(3,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[D(4)^4]3=D(4)wr3"],
[(3,12)(6,9),(3,9)(6,12),(1,7)(3,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,11)(2,10)(3,9)(4,8)(5,7),"1/2e[D(4)^3]S(3)"],
[(1,12),(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,7)(2,10)(3,11)(4,8)(5,9)(6,12),"[2^6]S_4(6c)=2wrS_4(6c)"],
[(3,6,9,12),(1,7)(3,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,11)(2,10)(3,9)(4,8)(5,7),"1/2c[D(4)^3]S(3)"],
[(1,12)(2,3),(1,7)(6,12),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(2,10)(3,11)(4,8)(5,9),"[2^5]2S_4(6)"],
[(1,12),(2,8)(3,9)(4,10)(5,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(2,10)(3,11)(4,8)(5,9),"[2^6]S_4(6d)=2wrS_4(6d)"],
[(3,12)(6,9),(3,9)(6,12),(3,6,12)(4,10,7),
(1,5,9)(2,6,4,8,12,7,11,3,10),"1/3[A(4)^3]3"],
[(3,12)(6,9),(3,9)(6,12),(3,6,12)(4,10,7),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[1/3.A(4)^3]3"],
[(1,12)(2,3),(1,3,5,7,9)(2,4,6,8,12),(1,11)(2,8)(3,9)(10,12),
"[2^5]L(6)"],
[(4,8,12),(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,10)(2,5)(6,9),
"[3^4]S(4)=3wrS(4)"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,7,10)(2,5,11)(3,6,9),
(2,8,7)(3,6,12)(4,11,10),"[3^4:2]A(4)_4"],
[(4,8,12),(2,8,11)(3,6,12)(4,7,10),(1,7,10)(2,5,11)(3,6,9),
(1,11)(2,10)(3,9)(4,8)(5,7),"1/2[3^4:2]S(4)"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(2,8,11)(3,6,12)(4,7,10),
(1,7,10)(2,5,11)(3,6,9),"[3^4:2]A(4)"],
[(1,12)(2,3),(2,6,10)(3,7,11),(1,3,5,7,9,11)(2,4,6,8,10,12),
(2,6)(3,7)(4,8)(5,9),(6,10)(7,11)(8,9),"[2^5]F_36:2_2{S_3^2,t}"],
[(1,12)(2,3),(1,5,9)(4,8,12),(4,8)(5,9),(1,7)(2,8)(3,9)(4,10)(5,11)
(6,12),"[2^5]F_36(6):2"],
[(1,12)(2,3),(2,6,10)(3,7,11),(4,8)(5,9),(1,3,5,7)(2,4,6,12)(8,10,9,11),
"[2^5]F_36:2_2{S_3^2,i}"],
[(1,12)(2,3),(2,6,10)(3,7,11),(1,3)(2,12)(4,6,8,10)(5,7,9,11),
(6,10)(7,11)(8,9),"[2^5]F_36:2_2{3^2:4}"],
[(3,12)(6,9),(3,9)(6,12),(2,8,11)(3,6,12)(4,7,10),(1,10)(2,5)(6,9),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),"[E(4)^3:3:2]3"]
,
[(1,12),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),(1,7)(2,8)(3,9)(4,10)
(5,11)(6,12),"[2^6]F_18:2=2wrF_18(6):2"],
[(1,12),(1,5,9)(4,8,12),(2,10)(3,11)(4,8)(5,9),
(1,7)(2,8,10,4)(3,9,11,5)(6,12),"[2^6]F_36=2wrF_36(6)"],
[(4,8,12),(4,8)(7,11),(2,10)(4,8),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[3^4:2^3]E(4)"],
[(4,8,12),(2,10)(4,8),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(3,9)(5,11)(6,10),"[3^4:2^2]D(4)_4"],
[(4,8,12),(2,10)(4,8),(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
(1,4,11,10,5,8,7,2)(3,6,9,12),"1/2[S(3)^4]4"],
[(4,8,12),(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12),"[3^4:2^3]4"],
[(4,8,12),(2,10)(4,8),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8,10,4)(3,9)(5,11)(6,12),"1/2[S(3)^4]E(4)"],
[(4,8,12),(2,10)(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,2)(3,12)(4,7)(5,10)(6,9)(8,11),"[3^4:2^2]D(4)_2"],
[(4,8,12),(2,10)(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,7)(3,9)(5,11),
"[3^4:2^2]D(4)"],
[(4,8,12),(2,10)(4,8),(2,8,10,4)(6,12),(1,12)(2,3)(4,5)(6,7)(8,9)
(10,11),"[F_36^2]2=F_36wr2"],
[(3,6,9,12),(3,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[D(4)^4]S(3)=D(4)wrS(3)"],
[(3,12)(6,9),(3,9)(6,12),(3,6,12)(4,10,7),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,7)(4,8)(6,9)(10,11),
"[1/3.A(4)^3]S(3)_2"],
[(3,12)(6,9),(3,9)(6,12),(3,6,12)(4,10,7),(1,5,9)(2,6,10)(3,7,11)
(4,8,12),(1,5)(2,10)(4,8)(7,11),"[1/3.A(4)^3]S(3)"],
[(3,12)(6,9),(3,9)(6,12),(1,10,7)(3,6,9),(2,11)(3,6)(7,10),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[E(4)^3:3^2:2]3"],
[(3,12)(6,9),(3,9)(6,12),(3,6,12)(4,10,7),(1,6)(3,7)(4,12)(8,11)(9,10),
(1,5)(2,7)(4,8)(6,9)(10,11),"[1/3.A(4)^3]S(3)_6"],
[(1,12),(1,3,5,7,9)(2,4,6,8,12),(1,11)(2,8)(3,9)(10,12),
"[2^6]L(6)=2wrL(6)"],
[(1,12)(2,3),(1,3,5,7,9)(2,4,6,8,12),(1,10,12,11)(2,4)(3,5)(6,8)(7,9)
,"1/2[2^6]L(6):2"],
[(1,12)(2,3),(1,3,5,7,9)(2,4,6,8,12),(1,11)(2,4)(3,5)(6,8)(7,9)
(10,12),"[2^5]L(6):2"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,10)(2,5)(6,9),"[3^4:2]S(4)"],
[(4,8,12),(1,5)(2,10)(4,8)(7,11),(1,7,10)(2,5,11)(3,6,9),
(3,12)(4,7)(6,10)(8,11),"[3^4:2]S(4)_8"],
[(6,12),(2,6,10)(4,8,12),(2,10)(4,8),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
"[2S_4^2]2=2S_4wr2"],
[(4,8,12),(4,8),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),"[S(3)^4]E(4)=S(3)wrE(4)"],
[(4,8,12),(2,10)(4,8),(2,8)(4,10)(6,12),(1,7)(3,9)(5,11),
(1,4,11,10,5,8,7,2)(3,6,9,12),"1/2[S(3)^4]dD(4)"],
[(4,8,12),(2,10)(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,7,5,11)(2,10)(3,9)(4,8),"1/2[S(3)^4]cD(4)"],
[(4,8,12),(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),"[S(3)^4]4=S(3)wr4"],
[(3,6,12),(3,6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[A(4)^3]3=A(4)wr3"],
[(4,8,12),(2,10)(4,8),(1,10)(2,5)(3,12)(4,7)(6,9)(8,11),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),(1,7,5,11)(2,10)(3,9)(4,8),
"1/2[S(3)^4]eD(4)"],
[(4,8,12),(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,7)(3,9)(5,11),
"[3^4:2^3]D(4)"],
[(3,12)(6,9),(3,9)(6,12),(1,10,7)(3,6,9),(2,11)(3,6)(7,10),
(1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,5)(2,10)(4,8)(7,11),
"[E(4)^3:3^2:2]S(3)"],
[(2,4,6,8,12),(2,8)(10,12),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
"[L(6)^2]2=L(6)wr2"],
[(1,12),(1,3,5,7,9)(2,4,6,8,12),(1,11)(2,4)(3,5)(6,8)(7,9)(10,12),
"[2^6]L(6):2=2wrL(6):2"],
[(4,8,12),(4,8)(7,11),(2,8,11)(3,6,12)(4,7,10),(1,7,10)(2,5,11)(3,6,9),
"[3^4:2^3]A(4)"],
[(1,7,3,10,5,9,6,12)(2,11,8,4),(1,6,3,9)(2,7,12,10,4,5,11,8),"M_11(12)"
],[(3,6,12),(3,6,9),(3,12)(4,7)(8,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"[1/4.S(4)^3]3"],
[(4,8,12),(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,7)(3,9)(5,11),
"[S(3)^4]D(4)=S(3)wrD(4)"],
[(3,6,12),(3,6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[A(4)^3]S(3)=A(4)wrS(3)"],
[(3,6,12),(3,6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(3,12)(4,11)(7,8),"1/2[1/4.S(4)^3]S(3)"],
[(1,12)(2,3),(1,3,5)(2,4,12),(2,4,6,8,10)(3,5,7,9,11),"[2^5]A(6)"],
[(2,4,6,8,12),(1,11)(2,4)(3,5)(6,8)(7,9)(10,12),
(1,12,11,10)(2,5,4,3)(6,9,8,7),"1/2[(L(6):2)^2]2"],
[(2,4,6,8,12),(1,11)(2,4)(3,5)(6,8)(7,9)(10,12),
(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),"[1/2.(L(6):2)^2]2"],
[(4,8,12),(4,8),(2,8,11)(3,6,12)(4,7,10),(1,7,10)(2,5,11)(3,6,9),
"[S(3)^4]A(4)=S(3)wrA(4)"],
[(4,8,12),(4,8)(7,11),(1,4,7,10)(2,5,8,11)(3,6,9,12),(2,11)(3,6)(7,10),
"[3^4:2^3]S(4)"],
[(4,8,12),(2,10)(4,8),(2,8,11)(3,6,12)(4,7,10),(1,7,10)(2,5,11)(3,6,9),
(1,7,5,11)(2,10)(3,9)(4,8),"1/2[S(3)^4]S(4)"],
[(3,6,12),(3,6,9),(3,12)(4,7)(8,11),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[1/4.S(4)^3]S(3)"],
[(3,6,12),(3,6,9),(3,12)(4,7),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
"[1/2.S(4)^3]3"],
[(1,12)(2,3),(1,3)(2,12),(1,3,5,7,9,11)(2,4,6,8,10,12),"[2^5]S(6)"],
[(1,12),(1,3,5)(2,4,12),(2,4,6,8,10)(3,5,7,9,11),"[2^6]A(6)=2wrA(6)"],
[(1,12)(2,3),(1,3,5)(2,4,12),(2,4,6,8,10)(3,5,7,9,11),(1,2,12,3),
"1/2[2^6]S(6)"],
[(2,4,6,8,12),(2,4)(6,8)(10,12),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
"[(L(6):2)^2]2=L(6):2wr2"],
[(4,8,12),(4,8),(1,4,7,10)(2,5,8,11)(3,6,9,12),(1,10)(2,5)(6,9),
"[S(3)^4]S(4)=S(3)wrS(4)"],
[(3,6,12),(3,6,9),(3,12)(4,7),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,5)(2,10)(4,8)(7,11),"[1/2.S(4)^3]S(3)"],
[(3,6,12),(3,6,9),(1,10)(6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,2)(4,8)(5,10)(6,9)(7,11),"1/2[S(4)^3]S(3)"],
[(3,6,9,12),(6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),"[S(4)^3]3=S(4)wr3"],
[(1,12),(1,3)(2,12),(1,3,5,7,9,11)(2,4,6,8,10,12),"[2^6]S(6)=2wrS(6)"],
[(3,6,9,12),(6,9),(1,5,9)(2,6,10)(3,7,11)(4,8,12),
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[(1,11,2,3,4)(5,8,12,6,7),(1,9,5,12,11,8,2,4)(6,10),"M(12)"],
[(2,4,12),(2,4,6,8,10),(1,12)(2,3)(4,5)(6,7)(8,9)(10,11),
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