Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q64×D103 |
| Fitting | Q64×C103 ⋊ C2 |
| Sylow | C103 ⋊ C2×Q64 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 3 generators on 167 points:
(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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(104,106,110,120)(105,111,115,136)(107,122,126,156)(108,128,130,162)(109,132,129,119)(112,138,140,165)(113,142,143,167)(114,144,131,135)(116,145,147,121)(117,137,133,124)(118,141,150,123)(125,160,158,155)(127,134,161,163)(139,166,152,149)(146,153,151,159)(148,157,154,164);(104,105,110,115)(106,116,120,147)(107,121,126,145)(108,127,130,161)(109,131,129,114)(111,133,136,117)(112,137,140,124)(113,141,143,123)(118,149,150,166)(119,151,132,146)(122,142,156,167)(125,159,158,153)(128,138,162,165)(134,160,163,155)(135,148,144,154)(139,157,152,164)1007 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 6813);