Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D53×#2180 |
| Fitting | C53×#2180 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2180 |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,6,5,7,18,23,20)(2,9,11,17,12,27,21,10)(3,14,22,19,15,31,16,32)(8,24,29,30,25,13,26,28)(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);(1,3)(2,8)(4,14)(5,19)(6,22)(7,15)(9,24)(10,28)(11,29)(12,25)(13,27)(16,23)(17,30)(18,31)(20,32)(21,26);(1,2)(3,13,15,24)(4,17)(5,9)(6,21)(7,12)(8,14,25,31)(10,18)(11,23)(16,28,22,30)(19,29,32,26)(20,27);(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)644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322997);