trans17.grp

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##
#W  trans17.grp        GAP transitive groups library        Alexander Hulpke
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##
#Y  Copyright (C)  1997,  Lehrstuhl D für Mathematik,  RWTH Aachen,  Germany
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##  This file contains the transitive groups of degree 17
##

TRANSGRP[17]:=
[[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17),"C(17)=17"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17),(2,17)(3,16)(4,15)(5,14)(6,13)
(7,12)(8,11)(9,10),"D(17)=17:2"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17),
(2,14,17,5)(3,10,16,9)(4,6,15,13)(7,11,12,8),"F_68(17)=17:4"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17),
(2,10,14,16,17,9,5,3)(4,11,6,12,15,8,13,7),"F_136(17)=17:8"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17),
(2,4,10,11,14,6,16,12,17,15,9,8,5,13,3,7),"F_272(17)=17:16"],
[(1,6,13,5,4,2,15,10,14,12,3,9,7,11,8),(1,16)(2,3)(4,5)(6,7)(8,9)(10,11)
(12,13)(14,15),(2,3)(4,9)(5,7)(6,8)(10,14)(11,13)(12,15)(16,17),
"L(17)=PSL(2,16)"],
[(1,6,13,5,4,2,15,10,14,12,3,9,7,11,8),(1,16)(2,3)(4,5)(6,7)(8,9)(10,11)
(12,13)(14,15),(1,7)(2,13)(3,10)(4,11)(5,12)(8,14),
(2,3)(4,9)(5,7)(6,8)(10,14)(11,13)(12,15)(16,17),"L(17):2=<PZL(2,16)"],
[(1,6,13,5,4,2,15,10,14,12,3,9,7,11,8),(1,16)(2,3)(4,5)(6,7)(8,9)(10,11)
(12,13)(14,15),(1,12,7,5)(2,4,13,11)(3,8,10,14)(6,9),
(2,3)(4,9)(5,7)(6,8)(10,14)(11,13)(12,15)(16,17),"L(17):4=PYL(2,16)"],
[(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17),(1,2,3),"A17"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17),(1,2),"S17"]];
TRANSPROPERTIES[17]:=[[17,1,1,1,"s2401"
,[7017],[15017],[39017]],
[34,1,1,1,
"01s2301"
,[7017],[-7034],[-15034,7017]],
[68,1,1,1,
"01s0702s1B01"
,[-3034],[-3068],[-7068,-3034]],
[136,1,1,1,
"01s0702s1308s0701"
,[-1068],[-1136],[-3136,-1068]],
[272,1,2,-1,
"01s0702s1308s0703"
,[-136],[-272],[-1272,-136]],
[4080,1,3,1,
"01s0202s0A08s1509"
,[136],[272],[680],[4,[340,2020]]],
[8160,1,3,1,
"05s0202s0402s0508s0402s0C01s0309"
,[136],[272],[680],[4,[-2020,340]]],
[16320,1,3,1,
"05s0202s0422s0508s0402s0808s0301s024009"
,[136],[272],[680],[4,[-2040,-340]]],
[177843714048000,1,15,1,
"55AAAAB654AAA56AA756B5549B55A95526AD2A966AAB55594D52AB135D6C9ACA95AAB26B29"
,[136],[272],[680],[4,[2380]]],
[355687428096000,1,17,-1,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
,[-136],[-272],[-680]]];