Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q64×C103 ⋊ C2 |
| Sylow | C103 ⋊ #2264 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 3 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)(105,112)(111,133)(113,136)(114,137)(115,131)(116,143)(121,142)(127,161)(134,163)(135,141)(138,164)(139,152)(140,165)(144,151)(148,167)(153,159);(104,106,110,120)(105,111,112,133)(107,122,126,156)(108,128,130,162)(109,132,129,119)(113,138,136,164)(114,140,137,165)(115,141,131,135)(116,142,143,121)(117,145,147,124)(118,149,150,123)(125,160,158,155)(127,134,161,163)(139,167,152,148)(144,153,151,159)(146,157,154,166);(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)(104,105)(106,116)(107,121)(108,127)(109,131)(110,112)(111,117)(113,124)(114,123)(115,129)(118,148)(119,151)(120,143)(122,140)(125,159)(126,142)(128,138)(130,161)(132,144)(133,147)(134,155)(135,154)(136,145)(137,149)(139,166)(141,146)(150,167)(152,157)(153,158)(156,165)(160,163)(162,164)Polycyclic presentation:
2^7,103|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^102,d^b=de,e^b=ef,f^b=fg,h^c=h^102995 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 6829);