Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D53×Q128 |
| Fitting | C53×Q128 ⋊ C2 |
| Sylow | C53 ⋊ C2×Q128 |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 181 points:
(1,3,8,20)(2,9,14,43)(4,22,27,75)(5,29,32,92)(6,34,36,96)(7,38,35,19)(10,45,48,109)(11,50,52,117)(12,54,55,119)(13,56,37,42)(15,57,60,21)(16,44,39,24)(17,49,65,23)(18,53,67,30)(25,82,84,128)(26,86,83,74)(28,40,89,102)(31,94,77,91)(33,41,95,104)(46,111,112,125)(47,113,97,108)(51,118,87,116)(58,122,123,81)(59,71,68,85)(61,110,99,127)(62,80,98,107)(63,120,124,69)(64,78,90,114)(66,121,126,70)(72,106,103,76)(73,105,100,79)(88,115,93,101)(129,130,132,134,136,138,140,142,144,146,148,150,152,154,156,158,160,162,164,166,168,170,172,174,176,178,180,181,179,177,175,173,171,169,167,165,163,161,159,157,155,153,151,149,147,145,143,141,139,137,135,133,131);(1,2,8,14)(3,15,20,60)(4,21,27,57)(5,28,32,89)(6,33,36,95)(7,37,35,13)(9,39,43,16)(10,44,48,24)(11,49,52,23)(12,53,55,30)(17,63,65,124)(18,66,67,126)(19,68,38,59)(22,50,75,117)(25,81,84,122)(26,85,83,71)(29,45,92,109)(31,93,77,88)(34,58,96,123)(40,100,102,73)(41,103,104,72)(42,62,56,98)(46,110,112,127)(47,80,97,107)(51,78,87,114)(54,99,119,61)(64,125,90,111)(69,106,120,76)(70,105,121,79)(74,118,86,116)(82,115,128,101)(91,113,94,108);(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(158,159)(160,161)(162,163)(164,165)(166,167)(168,169)(170,171)(172,173)(174,175)(176,177)(178,179)(180,181)980 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90616);