Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | D53×#2171 |
| Fitting | C53×#2171 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2171 |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,6,14,7,19,24,9,8,20,25,27,5,18,23,28)(2,10,12,29,11,22,30,32,13,3,15,17,21,16,31,26)(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)(2,9)(4,15)(5,22)(6,17)(7,16)(8,10)(11,27)(12,20)(13,28)(14,21)(18,30)(19,31)(23,32)(24,26)(25,29);(1,2,6,12,7,11,24,30,8,13,25,15,5,21,23,31)(3,14,17,19,16,9,26,20,10,27,29,18,22,28,32,4);(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)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322798);