Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C103 ⋊ #1420 |
70 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)(104,106,111,122)(105,112,116,138)(107,124,129,153)(108,121,110,119)(109,131,133,151)(113,140,143,149)(114,144,134,136)(115,145,146,147)(117,123,150,160)(118,127,154,164)(120,125,156,132)(126,162,128,161)(130,137,141,166)(135,139,152,163)(142,155,159,167)(148,165,157,158);(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)(104,105,108,114,111,116,110,134)(106,117,119,148,122,150,121,157)(107,123,126,158,129,160,128,165)(109,130,125,146,133,141,132,115)(112,135,136,118,138,152,144,154)(113,139,142,164,143,163,159,127)(120,155,151,140,156,167,131,149)(124,145,161,166,153,147,162,137)Polycyclic presentation:
2^7,103|a^2=d,b^2=g,c^2=efg,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=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^1022066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 2704);