Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D53×#2145 |
| Fitting | C53×#2145 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2145 |
1170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,6,18)(2,8,11,10)(3,13,15,16)(5,17,21,30)(7,22,23,27)(9,24,26,19)(12,28,29,25)(14,20,31,32)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,3)(2,7)(4,13)(5,20)(6,15)(8,22)(9,25)(10,27)(11,23)(12,24)(14,30)(16,18)(17,31)(19,29)(21,32)(26,28);(1,2)(3,12,15,29)(4,8)(5,19)(6,11)(7,14,23,31)(9,17)(10,18)(13,28,16,25)(20,27,32,22)(21,24)(26,30);(34,35)(36,37)(38,39)(40,41)(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)896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322507);