Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | D53×#1976 |
| Fitting | C53×#1976 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1976 |
1474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,5,15,6,16,18,29)(2,8,10,14,9,22,17,28)(3,11,13,25,12,24,26,30)(7,19,20,23,21,31,27,32)(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)(2,7,9,21)(4,11)(5,13)(6,12)(8,19,22,31)(10,20,17,27)(14,23,28,32)(15,25)(16,24)(18,26)(29,30);(1,2)(3,7,12,21)(4,14)(5,17)(6,9)(8,15)(10,18)(11,23,24,32)(13,27,26,20)(16,28)(19,30,31,25)(22,29);(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, 173538);