Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C157 ⋊ #1312 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 20096 |
A minimal faithful permutation representation — 2 generators on 181 points:
(1,2,7,4)(3,11,14,9)(5,16,13,6)(8,24,23,18)(10,29,26,15)(12,20,27,22)(17,41,36,31)(19,46,43,28)(21,37,40,35)(25,33,44,39)(30,62,53,48)(32,67,64,45)(34,58,57,52)(38,54,61,56)(42,50,65,60)(47,87,74,69)(49,92,89,66)(51,83,78,73)(55,79,82,77)(59,75,86,81)(63,71,90,85)(68,116,99,94)(70,121,118,91)(72,112,103,98)(76,108,107,102)(80,104,111,106)(84,100,115,110)(88,96,119,114)(93,142,128,123)(95,147,144,120)(97,140,132,127)(101,138,134,131)(105,136,130,135)(109,133,126,137)(113,129,122,139)(117,125,145,141)(124,149,152,146)(143,148,154,151)(150,155,157,153)(159,162)(163,165)(166,167,168,171,169,172,174,177,170,173,175,178,176,179,180,181);(2,3)(4,6)(5,8)(7,12)(9,15)(10,17)(11,13)(14,21)(16,25)(18,28)(19,30)(20,26)(22,24)(23,34)(27,38)(29,42)(31,45)(32,47)(33,43)(35,41)(36,51)(37,39)(40,55)(44,59)(46,63)(48,66)(49,68)(50,64)(52,62)(53,72)(54,60)(56,58)(57,76)(61,80)(65,84)(67,88)(69,91)(70,93)(71,89)(73,87)(74,97)(75,85)(77,83)(78,101)(79,81)(82,105)(86,109)(90,113)(92,117)(94,120)(95,122)(96,118)(98,116)(99,126)(100,114)(102,112)(103,130)(104,110)(106,108)(107,134)(111,132)(115,128)(119,124)(121,143)(123,146)(125,144)(127,142)(129,141)(131,140)(133,139)(135,138)(136,137)(145,150)(147,153)(148,152)(149,151)(154,156)(155,157)(158,159,160,163,161,162,164,165)Polycyclic presentation:
2^7,157|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^156,h^b=h^129,h^d=h^1561328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 19425);