Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D53×#1636 |
| Fitting | C53×#1636 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1636 |
914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57,59,58)(55,61,62,66)(56,64,65,67)(60,68,69,63)(70,73,76,72)(71,77,80,85)(74,82,75,83)(78,84,79,81);(54,56)(55,60)(57,64)(58,67)(59,65)(61,68)(62,69)(63,66)(70,72,76,73)(71,77,80,85)(74,83,75,82)(78,84,79,81);(54,55,59,62)(56,63,65,68)(57,61,58,66)(60,67,69,64)(70,71,76,80)(72,81,73,84)(74,79,75,78)(77,83,85,82);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 145301);