Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D53×#2221 |
| Fitting | C53×#2221 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2221 |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,3)(2,10)(4,15)(5,19)(6,14)(7,16)(8,20)(9,24)(11,28)(12,26)(13,27)(17,30)(18,29)(21,32)(22,25)(23,31)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,2,9,22,6,12,18,23,7,13,17,21,5,11,4,8)(3,10,24,25,14,26,29,31,16,27,30,32,19,28,15,20);(2,8)(3,14)(4,9)(5,6)(10,25)(11,22)(12,21)(13,23)(15,29)(16,19)(17,18)(20,26)(27,32)(28,31);(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)728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324121);