Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C32×C103 ⋊ C2 |
| Sylow | C103 ⋊ #1417 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 2 generators on 167 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)(104,106)(105,111)(107,124)(108,119)(109,131)(110,122)(112,138)(113,134)(114,143)(115,145)(116,136)(117,123)(118,127)(120,125)(121,129)(126,157)(128,159)(130,135)(132,150)(133,137)(139,151)(140,166)(141,165)(142,163)(144,167)(146,154)(147,156)(148,164)(149,162)(152,160)(153,155)(158,161);(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)(104,105,108,113,110,116,129,115)(106,117,119,146,122,147,121,153)(107,123,126,154,128,156,161,155)(109,130,125,114,132,142,160,144)(111,133,134,149,136,148,145,118)(112,137,139,162,141,164,140,127)(120,151,150,165,152,166,131,138)(124,143,157,163,159,167,158,135)Polycyclic presentation:
2^7,103|a^2=d,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^102,c^b=ce,e^b=ef,f^b=fg,h^b=h^1023302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 2695);