Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD64×C101 ⋊ C2 |
| Sylow | C101 ⋊ #2262 |
106 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 165 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 3 generators on 165 points:
(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(102,105,108,123)(103,110,114,113)(104,116,120,119)(106,121,127,154)(107,122,130,155)(109,131,133,141)(111,134,138,137)(112,135,140,128)(115,142,143,150)(117,144,147,146)(118,145,149,129)(124,151,157,156)(125,152,159,158)(126,153,160,163)(132,139,161,165)(136,148,162,164);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,104)(103,109)(105,116)(106,125)(107,129)(108,120)(110,131)(111,136)(112,139)(113,141)(114,133)(115,124)(117,126)(118,122)(119,123)(121,152)(127,159)(128,132)(130,145)(134,148)(135,161)(137,164)(138,162)(140,165)(142,151)(143,157)(144,153)(146,163)(147,160)(149,155)(150,156)(154,158);(102,103)(104,115)(105,110)(106,124)(107,128)(108,114)(109,117)(111,126)(112,122)(113,123)(116,142)(118,148)(119,150)(120,143)(121,151)(125,139)(127,157)(129,136)(130,135)(131,144)(132,158)(133,147)(134,153)(137,163)(138,160)(140,155)(141,146)(145,162)(149,164)(152,161)(154,156)(159,165)Polycyclic presentation:
2^7,101|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^100,h^c=h^100988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 6818);