Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic1552 |
| Sylow | C97 ⋊ C2×Q64 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 12416 |
A minimal faithful permutation representation — 3 generators on 163 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)(100,102,106,116)(101,107,111,132)(103,118,122,152)(104,124,126,158)(105,128,125,115)(108,134,136,161)(109,138,139,163)(110,140,127,131)(112,141,143,117)(113,133,129,120)(114,137,146,119)(121,156,154,151)(123,130,157,159)(135,162,148,145)(142,149,147,155)(144,153,150,160);(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)(100,101,106,111)(102,112,116,143)(103,117,122,141)(104,123,126,157)(105,127,125,110)(107,129,132,113)(108,133,136,120)(109,137,139,119)(114,145,146,162)(115,147,128,142)(118,138,152,163)(121,155,154,149)(124,134,158,161)(130,156,159,151)(131,144,140,150)(135,153,148,160);(98,99)3110 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 6815);