Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #452×C97 ⋊ C2 |
| Sylow | C97 ⋊ #3011 |
700 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 4 generators on 133 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)(105,116)(109,123)(113,127)(117,129)(121,132)(124,130)(126,133)(128,131);(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)(99,101)(102,105)(103,109)(104,113)(106,117)(107,116)(108,121)(110,124)(111,123)(112,126)(114,128)(115,127)(118,130)(119,131)(120,129)(122,132)(125,133);(102,104,107,115)(103,108,111,122)(105,113,116,127)(106,119,120,114)(109,121,123,132)(110,125,118,112)(117,131,129,128)(124,133,130,126);(98,99)(100,101)(102,103,107,111)(104,112,115,125)(105,109,116,123)(106,118,120,110)(108,119,122,114)(113,126,127,133)(117,130,129,124)(121,131,132,128)Polycyclic presentation:
2^7,97|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,d^c=dg,h^c=h^96,h^d=h^96944 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 13802);