Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D53×#1953 |
| Fitting | C53×#1953 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1953 |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,5,18,7,20,6,19)(2,9,10,17,11,25,21,31)(3,13,15,28,16,29,14,27)(8,22,23,30,24,32,12,26)(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);(1,3,6,14,7,16,5,15)(2,8,10,23,11,24,21,12)(4,13,19,27,20,29,18,28)(9,22,17,30,25,32,31,26);(1,2,6,10,7,11,5,21)(3,12,14,8,16,23,15,24)(4,17,19,25,20,31,18,9)(13,22,27,30,29,32,28,26);(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, 173132);