Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D53×#1664 |
| Fitting | C53×#1664 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1664 |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
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)(54,56)(55,60)(57,65)(58,67)(59,66)(61,64)(62,69)(63,68)(70,72,74,79)(71,75,77,84)(73,82,80,78)(76,85,81,83);(54,56)(55,60)(57,67)(58,65)(59,66)(61,69)(62,64)(63,68)(70,71,74,77)(72,75,79,84)(73,81,80,76)(78,85,82,83);(54,55,59,63)(56,64,66,69)(57,62,58,61)(60,67,68,65)(72,78)(73,80)(75,83)(76,81)(79,82)(84,85);(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)560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150734);