Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q64×D97 |
| Fitting | Q64×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×Q64 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 3 generators on 161 points:
(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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(98,100,104,114)(99,105,109,130)(101,116,120,150)(102,122,124,156)(103,126,123,113)(106,132,134,159)(107,136,137,161)(108,138,125,129)(110,139,141,115)(111,131,127,118)(112,135,144,117)(119,154,152,149)(121,128,155,157)(133,160,146,143)(140,147,145,153)(142,151,148,158);(98,99,104,109)(100,110,114,141)(101,115,120,139)(102,121,124,155)(103,125,123,108)(105,127,130,111)(106,131,134,118)(107,135,137,117)(112,143,144,160)(113,145,126,140)(116,136,150,161)(119,153,152,147)(122,132,156,159)(128,154,157,149)(129,142,138,148)(133,151,146,158)950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 6813);