Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | D53×#2103 |
| Fitting | C53×#2103 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2103 |
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:
(1,4,5,19,6,20,7,21)(2,9,10,26,11,17,22,31)(3,13,14,28,16,29,15,18)(8,23,12,25,24,32,27,30)(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);(1,3,7,14,6,16,5,15)(2,8,22,12,11,24,10,27)(4,18,21,13,20,28,19,29)(9,25,31,32,17,30,26,23);(1,2,5,10,6,11,7,22)(3,12,14,24,16,27,15,8)(4,17,19,31,20,9,21,26)(13,25,28,32,29,30,18,23);(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, 199543);