Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | D53×#2229 |
| Fitting | C53×#2229 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2229 |
542 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 points:
(9,11,12,20)(10,16,15,30)(13,26,23,40)(14,29,24,22)(17,35,31,39)(18,36,28,33)(19,38,37,25)(21,34,32,27)(41,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43);(1,3,4,8)(2,5,6,7)(10,15)(16,30)(17,31)(18,28)(19,37)(25,38)(33,36)(35,39);(1,2,4,6)(3,7,8,5)(9,10,12,15)(11,19,20,37)(13,25,23,38)(14,28,24,18)(16,32,30,21)(17,34,31,27)(22,39,29,35)(26,36,40,33);(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)(86,87)(88,89)(90,91)(92,93)812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324199);