trans15.grp

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##
#W  trans15.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 15
##  They were originally published by Greg Butler
##  Names and actual generators are by John Conway, John McKay and AH.
##

TRANSGRP[15]:=
[[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),"C(15)=5[x]3"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)
(7,8),"D(15)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),
"D(5)[x]3"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,11)(2,7)(4,14)(5,10)(8,13),
"5[x]S(3)"],
[(1,9,10,3,14)(2,15,7,12,6)(4,5,11,13,8),(1,4,10)(2,5,8)(3,7,11)(6,9,15)
(12,14,13),"A_5(15)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),
(1,2,4,8)(3,6,12,9)(5,10)(7,14,13,11),"F(5)[1/2]S(3)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),
(1,11)(2,7)(4,14)(5,10)(8,13),"D(5)[x]S(3)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,7,4,13)(2,14,8,11)(3,6,12,9),
"F(5)[x]3"],
[(1,13,10,7,4)(2,5,8,11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
"[5^2]3"],
[(1,9,10,3,14)(2,15,7,12,6)(4,5,11,13,8),(1,4,10)(2,5,8)(3,7,11)(6,9,15)
(12,14,13),(1,4)(2,6)(3,7)(5,15)(8,9)(12,13),"S_5(15)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,7,4,13)(2,14,8,11)(3,6,12,9),
(1,11)(2,7)(4,14)(5,10)(8,13),"F(5)[x]S(3)"],
[(1,13,10,7,4)(2,5,8,11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),"[5^2:2]3"],
[(1,13,10,7,4)(2,5,8,11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,11)(2,7)(4,14)(5,10)(8,13),"[5^2]S(3)"],
[(1,13,10,7,4)(2,5,8,11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8),"5^2:2[1/2]S(3)"],
[(1,9,10,3,14)(2,15,7,12,6)(4,5,11,13,8),(1,4,10)(2,5,8)(3,7,11)(6,9,15)
(12,14,13),(1,2,15)(4,5,6)(8,9,10)(12,13,14),"3A_5(15)=[3]A(5)=GL(2,4)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,13)(2,14)(3,6)(4,7)(8,11)(9,12),
"A(5)[x]3"],
[(1,13,10,7,4)(2,5,8,11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),(1,2,4,8)(3,6,12,9)(5,10)
(7,14,13,11),"1/2[5^2:4]S(3)"],
[(1,13,10,7,4)(2,5,8,11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),(1,11)(2,7)(4,14)(5,10)(8,13),
"[5^2:2]S(3)"],
[(1,13,10,7,4)(2,5,8,11,14),(1,7,4,13)(2,14,8,11)(3,6,12,9),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),"[5^2:4]3"],
[(1,9,10,3,14)(2,15,7,12,6)(4,5,11,13,8),(1,5)(2,7)(3,6)(4,15)(8,9)
(12,13),"A_6(15)"],
[(1,9,10,3,14)(2,15,7,12,6)(4,5,11,13,8),(1,4,10)(2,5,8)(3,7,11)(6,9,15)
(12,14,13),(1,4)(2,6)(3,7)(5,15)(8,9)(12,13),
(1,2,15)(4,5,6)(8,9,10)(12,13,14),"3S_5(15)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,14)(2,7)(4,11)(5,10)(6,9)(8,13),
"S(5)[1/2]S(3)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,13)(2,14)(3,6)(4,7)(8,11)(9,12),
(1,11)(2,7)(4,14)(5,10)(8,13),"A(5)[x]S(3)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,4)(6,9)(11,14),"S(5)[x]3"],
[(3,6,9,12,15),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),"[5^3]3=5wr3"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),"[3^4]5"],
[(1,13,10,7,4)(2,5,8,11,14),(1,7,4,13)(2,14,8,11)(3,6,12,9),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),
"[5^2:4]S(3)"],
[(1,9,10,3,14)(2,15,7,12,6)(4,5,11,13,8),(1,5)(2,7)(3,6)(4,15)(8,9)
(12,13),(1,4)(2,6)(3,7)(5,15)(8,9)(12,13),"S_6(15)"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15),(1,4)(6,9)(11,14),
(1,11)(2,7)(4,14)(5,10)(8,13),"S(5)[x]S(3)"],
[(3,6,9,12,15),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),"[5^3:2]3"],
[(3,6,9,12,15),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2[5^3:2]S(3)"],
[(3,6,9,12,15),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,11)(2,7)(4,14)(5,10)(8,13),"[5^3]S(3)"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,11)(2,7)(4,14)(5,10)(8,13),"[3^4:2]5"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),"[3^4]D(5)"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2[3^4:2]D(5)"],
[(5,10,15),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),"[3^5]5=3wr5"],
[(3,6,9,12,15),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),(1,2,4,8)(3,6,12,9)(5,10)
(7,14,13,11),"1/2[5^3:4]S(3)"],
[(3,6,9,12,15),(1,7,4,13)(2,14,8,11)(3,6,12,9),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),"[5^3:4]3"],
[(3,6,9,12,15),(1,4)(2,8)(7,13)(11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)
(5,10,15),"[1/2.D(5)^3]3"],
[(3,6,9,12,15),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),
"[5^3:2]S(3)"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,7,4,13)(2,14,8,11)(3,6,12,9),"[3^4]F(5)"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,2,4,8)(3,6,12,9)(5,10)(7,14,13,11),"1/2[3^4:2]F(5)"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,11)(2,7)(4,14)(5,10)(8,13),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),
"[3^4:2]D(5)"],
[(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),(1,4,7,10,13)(2,5,8,11,14)
(3,6,9,12,15),"[3^5:2]5"],
[(5,10,15),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2[3^5:2]D(5)"],
[(5,10,15),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),"[3^5]D(5)=3wrD(5)"],
[(1,9,10,3,14)(2,15,7,12,6)(4,5,11,13,8),(1,2,3)(5,6,7)(8,10,9)(12,14,13),
"A_7(15)"],
[(3,6,9,12,15),(1,4)(2,8)(7,13)(11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)
(5,10,15),(1,11)(2,7)(3,12)(4,14)(5,10)(6,9)(8,13),"1/2[D(5)^3]S(3)"],
[(3,6,9,12,15),(1,7,4,13)(2,14,8,11)(3,6,12,9),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),
"[5^3:4]S(3)"],
[(3,6,9,12,15),(3,12)(6,9),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
"[D(5)^3]3=D(5)wr3"],
[(3,6,9,12,15),(1,4)(2,8)(7,13)(11,14),(1,6,11)(2,7,12)(3,8,13)(4,9,14)
(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),"[1/2.D(5)^3]S(3)"],
[(1,6,11)(4,14,9),(1,11)(2,7)(4,14)(5,10)(8,13),(1,4,7,10,13)(2,5,8,11,14)
(3,6,9,12,15),(1,7,4,13)(2,14,8,11)(3,6,12,9),"[3^4:2]F(5)"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,13)(2,14)(3,6)(4,7)(8,11)(9,12),"[3^4]A(5)"],
[(5,10,15),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,2,4,8)(3,6,12,9)(5,10)(7,14,13,11),"1/2[3^5:2]F(5)"],
[(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),(1,4,7,10,13)(2,5,8,11,14)
(3,6,9,12,15),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),"[3^5:2]D(5)"],
[(5,10,15),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,7,4,13)(2,14,8,11)(3,6,12,9),"[3^5]F(5)=3wrF(5)"],
[(3,6,9,12,15),(1,13,4,7)(2,14,8,11),(1,6,11)(2,7,12)(3,8,13)(4,9,14)
(5,10,15),"[1/4.F(5)^3]3"],
[(3,6,9,12,15),(3,12)(6,9),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,2,4,8)(3,6,12,9)(5,10)(7,14,13,11),"1/2[D(5)^3:2]S(3)"],
[(3,6,9,12,15),(3,12)(6,9),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,7,4,13)(2,14,8,11)(3,6,12,9),"[D(5)^3:2]3"],
[(3,6,9,12,15),(3,12)(6,9),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,11)(2,7)(4,14)(5,10)(8,13),"[D(5)^3]S(3)=D(5)wrS(3)"],
[(1,6,11)(4,14,9),(1,11)(2,7)(4,14)(5,10)(8,13),(1,4,7,10,13)(2,5,8,11,14)
(3,6,9,12,15),(1,13)(2,14)(3,6)(4,7)(8,11)(9,12),"[3^4:2]A(5)"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,14)(2,7)(4,11)(5,10)(6,9)(8,13),"1/2[3^4:2]S(5)"],
[(1,6,11)(4,14,9),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(6,9)(11,14),"[3^4]S(5)"],
[(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),(1,4,7,10,13)(2,5,8,11,14)
(3,6,9,12,15),(1,7,4,13)(2,14,8,11)(3,6,12,9),"[3^5:2]F(5)"],
[(3,6,9,12,15),(1,13,4,7)(2,14,8,11),(1,6,11)(2,7,12)(3,8,13)(4,9,14)
(5,10,15),(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8),"1/2[1/2.F(5)^3]S(3)"],
[(3,6,9,12,15),(1,13,4,7)(2,14,8,11),(1,6,11)(2,7,12)(3,8,13)(4,9,14)
(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),"[1/4.F(5)^3]S(3)"],
[(3,6,9,12,15),(1,13,4,7)(2,14,8,11),(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),"[1/2.F(5)^3]3"],
[(3,6,9,12,15),(3,12)(6,9),(1,7,4,13)(2,14,8,11)(3,6,12,9),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),
"[D(5)^3:2]S(3)"],[(5,10,15),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,13)(2,14)(3,6)(4,7)(8,11)(9,12),"[3^5]A(5)=3wrA(5)"],
[(1,6,11)(4,14,9),(1,11)(2,7)(4,14)(5,10)(8,13),(1,4,7,10,13)(2,5,8,11,14)
(3,6,9,12,15),(1,4)(6,9)(11,14),"[3^4:2]S(5)"],
[(5,10,15),(1,11)(4,14),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
"[1/2.S(3)^5]5"],
[(1,9,10,3,14)(2,15,7,12,6)(4,5,11,13,8),(1,2,15)(4,5,6)(8,9,10)(12,13,14),
(1,5)(2,7)(3,6)(4,15)(8,9)(12,13),"L(15)=A_8(15)=PSL(4,2)"],
[(3,6,9,12,15),(3,12)(6,9),(1,7,4,13)(2,14,8,11),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),(1,11)(2,7)(3,6,12,9)(4,14)
(5,10)(8,13),"1/2[F(5)^3]S(3)"],
[(3,6,9,12,15),(3,12)(6,9),(1,7,4,13)(2,14,8,11),
(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),
"[1/2.F(5)^3]S(3)"],
[(3,6,9,12,15),(3,6,12,9),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
"[F(5)^3]3=F(5)wr3"],
[(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),(1,4,7,10,13)(2,5,8,11,14)
(3,6,9,12,15),(1,13)(2,14)(3,6)(4,7)(8,11)(9,12),"[3^5:2]A(5)"],
[(5,10,15),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,14)(2,7)(4,11)(5,10)(6,9)(8,13),"1/2[3^5:2]S(5)"],
[(5,10,15),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),(1,4)(6,9)(11,14),
"[3^5]S(5)=3wrS(5)"],
[(5,10,15),(1,11)(4,14),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(2,8)(3,12)(5,10)(6,9)(7,13)(11,14),"1/2[S(3)^5]D(5)"],
[(5,10,15),(1,11)(4,14),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),"[1/2.S(3)^5]D(5)"],
[(5,10,15),(5,10),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
"[S(3)^5]5=S(3)wr5"],
[(3,6,9,12,15),(3,6,12,9),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
(1,11)(2,7)(4,14)(5,10)(8,13),"[F(5)^3]S(3)=F(5)wrS(3)"],
[(5,10,15),(1,11)(2,7)(4,14)(5,10)(8,13),(1,4,7,10,13)(2,5,8,11,14)
(3,6,9,12,15),(1,4)(6,9)(11,14),"[3^5:2]S(5)"],
[(5,10,15),(1,11)(4,14),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),(1,2,4,8)(3,6,12,9)(5,10)
(7,14,13,11),"1/2[S(3)^5]F(5)"],
[(5,10,15),(1,11)(4,14),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,7,4,13)(2,14,8,11)(3,6,12,9),"[1/2.S(3)^5]F(5)"],
[(5,10,15),(5,10),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(2,8)(3,12)(6,9)(7,13)(11,14),"[S(3)^5]D(5)=S(3)wrD(5)"],
[(5,10,15),(5,10),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,7,4,13)(2,14,8,11)(3,6,12,9),"[S(3)^5]F(5)=S(3)wrF(5)"],
[(5,10,15),(1,11)(4,14),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,13)(2,14)(3,6)(4,7)(8,11)(9,12),"[1/2.S(3)^5]A(5)"],
[(5,10,15),(1,11)(4,14),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(5,10)(6,9)(11,14),"1/2[S(3)^5]S(5)"],
[(5,10,15),(5,10),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,13)(2,14)(3,6)(4,7)(8,11)(9,12),"[S(3)^5]A(5)=S(3)wrA(5)"],
[(5,10,15),(1,11)(4,14),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
(1,4)(6,9)(11,14),"[1/2.S(3)^5]S(5)"],
[(3,6,9,12,15),(3,6)(9,12),(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),
"[A(5)^3]3=A(5)wr3"],
[(5,10,15),(5,10),(1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15),
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