Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#20261551 |
| Fitting | C2×#137×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×#578 |
1408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 5 generators on 131 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)(103,114)(107,121)(111,125)(115,127)(119,130)(122,128)(124,131)(126,129);(100,103)(101,107)(102,111)(104,115)(105,114)(106,119)(108,122)(109,121)(110,124)(112,126)(113,125)(116,128)(117,129)(118,127)(120,130)(123,131);(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)(100,102,105,113)(101,106,109,120)(103,111,114,125)(104,117,118,112)(107,119,121,130)(108,123,116,110)(115,129,127,126)(122,131,128,124);(100,101,105,109)(102,110,113,123)(103,107,114,121)(104,116,118,108)(106,117,120,112)(111,124,125,131)(115,128,127,122)(119,129,130,126);(98,99)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 19276);