Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | D53×#2166 |
| Fitting | C53×#2166 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2166 |
538 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(2,8,9,11)(3,13)(4,17)(7,20,12,23)(10,27,25,24)(15,28)(18,22)(21,32,26,31)(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);(1,3)(2,7)(4,16)(5,15)(6,13)(8,23)(9,12)(10,26)(11,20)(14,17)(18,30)(19,28)(21,25)(22,29)(24,31)(27,32);(1,2,4,10,5,11,18,27,6,9,17,25,19,8,22,24)(3,12,14,26,15,23,29,32,13,7,16,21,28,20,30,31);(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)896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322691);