Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #362×C103 ⋊ C2 |
| Sylow | C103 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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)(104,107,111,126)(105,113,117,139)(106,119,122,151)(108,124,131,158)(109,132,110,125)(112,135,137,163)(114,138,142,155)(115,143,116,123)(118,145,146,166)(120,148,134,161)(121,150,133,149)(127,154,141,165)(128,156,159,167)(129,160,130,157)(136,162,144,153)(140,164,152,147);(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)(104,106)(105,112)(107,119)(108,128)(109,121)(110,133)(111,122)(113,135)(114,140)(115,136)(116,144)(117,137)(118,127)(120,130)(123,153)(124,156)(125,149)(126,151)(129,134)(131,159)(132,150)(138,164)(139,163)(141,146)(142,152)(143,162)(145,154)(147,155)(148,157)(158,167)(160,161)(165,166);(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)(104,105,111,117)(106,118,122,146)(107,123,126,143)(108,127,131,141)(109,116,110,115)(112,134,137,120)(113,132,139,125)(114,129,142,130)(119,147,151,164)(121,152,133,140)(124,155,158,138)(128,144,159,136)(135,156,163,167)(145,150,166,149)(148,153,161,162)(154,160,165,157)Polycyclic presentation:
2^7,103|a^2=g,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^102,d^b=df,f^b=fg,h^b=h^102,e^c=eg,h^c=h^102839 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 6491);