Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic1648 |
| Sylow | C103 ⋊ C2×Q64 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 3 generators on 169 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)(97,98)(99,100)(101,102)(106,108,112,122)(107,113,117,138)(109,124,128,158)(110,130,132,164)(111,134,131,121)(114,140,142,167)(115,144,145,169)(116,146,133,137)(118,147,149,123)(119,139,135,126)(120,143,152,125)(127,162,160,157)(129,136,163,165)(141,168,154,151)(148,155,153,161)(150,159,156,166);(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)(100,101)(102,103)(106,107,112,117)(108,118,122,149)(109,123,128,147)(110,129,132,163)(111,133,131,116)(113,135,138,119)(114,139,142,126)(115,143,145,125)(120,151,152,168)(121,153,134,148)(124,144,158,169)(127,161,160,155)(130,140,164,167)(136,162,165,157)(137,150,146,156)(141,159,154,166);(104,105)3302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 6815);