Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D53×#2080 |
| Fitting | C53×#2080 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2080 |
906 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,5,16,6,17,19,30)(2,8,9,22,10,23,25,32)(3,12,13,28,14,15,18,29)(7,20,11,26,21,31,24,27)(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)(4,15)(5,18)(6,14)(8,20)(9,24)(10,21)(11,25)(12,17)(13,19)(16,28)(22,27)(23,31)(26,32)(29,30);(1,2)(3,11,14,24)(4,8)(5,9)(6,10)(7,13,21,18)(12,27,15,26)(16,22)(17,23)(19,25)(20,29,31,28)(30,32);(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, 198485);