Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | D53×#2170 |
| Fitting | C53×#2170 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2170 |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,6,13,5,18,20,24,7,19,22,26,21,32,25,8)(2,3,10,15,11,16,28,30,12,17,29,31,9,14,27,23)(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)(4,10)(5,16)(6,15)(7,17)(9,26)(11,13)(12,24)(14,21)(18,28)(19,29)(20,30)(22,31)(23,25)(27,32);(1,2,6,10,5,11,20,28,7,12,22,29,21,9,25,27)(3,13,15,18,16,24,30,19,17,26,31,32,14,8,23,4);(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)1568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322792);