Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D53×#1868 |
| Fitting | C53×#1868 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1868 |
1342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57)(55,61)(56,64)(58,68)(59,67)(60,70)(62,74)(63,73)(65,77)(66,78)(69,80)(71,76)(72,82)(75,84)(79,81)(83,85);(54,56,58,66,59,65,69,79)(55,60,62,72,63,71,75,83)(57,64,68,78,67,77,80,81)(61,70,74,82,73,76,84,85);(54,55,58,62,59,63,69,75)(56,60,66,72,65,71,79,83)(57,61,68,74,67,73,80,84)(64,76,78,85,77,70,81,82);(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)896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 170670);