Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | D53×#2242 |
| Fitting | C53×#2242 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2242 |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,6)(5,8)(9,12,13,28,32,25,14,27,16,30,33,26,15,29,24,11)(10,18,19,37,35,40,20,17,22,23,34,39,21,36,31,38)(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);(1,3,4,7)(2,5,6,8)(9,11,24,29,15,26,33,30,16,27,14,25,32,28,13,12)(10,17,31,40,21,37,34,18,22,38,20,36,35,39,19,23);(1,2)(3,5)(4,6)(7,8)(9,10)(11,23)(12,17)(13,31)(14,34)(15,35)(16,22)(18,27)(19,24)(20,33)(21,32)(25,37)(26,36)(28,40)(29,39)(30,38);(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)1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324859);