Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 3 generators on 173 points:
(1,2,7,3)(4,11,14,8)(5,16,12,6)(9,24,23,17)(10,29,25,15)(13,20,27,21)(18,41,36,30)(19,46,42,28)(22,37,40,34)(26,33,44,38)(31,62,53,47)(32,67,63,45)(35,58,57,51)(39,54,61,55)(43,50,65,59)(48,87,74,68)(49,92,88,66)(52,83,78,72)(56,79,82,76)(60,75,86,80)(64,71,90,84)(69,116,99,93)(70,121,117,91)(73,112,103,97)(77,108,107,101)(81,104,111,105)(85,100,115,109)(89,96,119,113)(94,142,128,122)(95,147,143,120)(98,140,132,126)(102,138,135,130)(106,136,131,134)(110,133,127,137)(114,129,123,139)(118,125,145,141)(124,149,152,146)(144,148,154,150)(151,155,156,153)(158,160,161,165,162,159,163,164);(2,4)(3,6)(5,9)(7,13)(8,15)(10,18)(11,12)(14,22)(16,26)(17,28)(19,31)(20,25)(21,24)(23,35)(27,39)(29,43)(30,45)(32,48)(33,42)(34,41)(36,52)(37,38)(40,56)(44,60)(46,64)(47,66)(49,69)(50,63)(51,62)(53,73)(54,59)(55,58)(57,77)(61,81)(65,85)(67,89)(68,91)(70,94)(71,88)(72,87)(74,98)(75,84)(76,83)(78,102)(79,80)(82,106)(86,110)(90,114)(92,118)(93,120)(95,123)(96,117)(97,116)(99,127)(100,113)(101,112)(103,131)(104,109)(105,108)(107,135)(111,132)(115,128)(119,124)(121,144)(122,146)(125,143)(126,142)(129,141)(130,140)(133,139)(134,138)(136,137)(145,151)(147,153)(148,152)(149,150)(154,157)(155,156)(166,167,169,171)(168,173,172,170);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,146)(99,126,127,142)(103,130,131,140)(107,134,135,138)(111,137,132,136)(115,139,128,133)(119,141,124,129)(121,143,144,125)(145,150,151,149)(147,152,153,148)(154,156,157,155)(158,159,161,164,162,160,163,165)(167,170)(168,172)(171,173)Polycyclic presentation:
2^7,157|a^2=e,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^129,d^b=df,h^b=h^156,h^c=h^129,h^e=h^156602 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 20093);