Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C32×C97 ⋊ C2 |
| Sylow | C97 ⋊ #1417 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 2 generators on 161 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)(98,100)(99,105)(101,118)(102,113)(103,125)(104,116)(106,132)(107,128)(108,137)(109,139)(110,130)(111,117)(112,121)(114,119)(115,123)(120,151)(122,153)(124,129)(126,144)(127,131)(133,145)(134,160)(135,159)(136,157)(138,161)(140,148)(141,150)(142,158)(143,156)(146,154)(147,149)(152,155);(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)(98,99,102,107,104,110,123,109)(100,111,113,140,116,141,115,147)(101,117,120,148,122,150,155,149)(103,124,119,108,126,136,154,138)(105,127,128,143,130,142,139,112)(106,131,133,156,135,158,134,121)(114,145,144,159,146,160,125,132)(118,137,151,157,153,161,152,129)Polycyclic presentation:
2^7,97|a^2=d,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^96,c^b=ce,e^b=ef,f^b=fg,h^b=h^963110 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 2695);