Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | D53×#2117 |
| Fitting | C53×#2117 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2117 |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(2,9)(8,23)(10,12)(11,25)(13,26)(24,28)(27,29)(30,32)(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)(2,8)(4,17)(5,19)(6,14)(7,16)(9,23)(10,26)(11,28)(12,13)(15,21)(18,31)(20,22)(24,25)(27,30)(29,32);(1,2,5,11,6,12,20,29,7,9,21,25,4,10,18,27)(3,13,15,30,14,23,31,28,16,26,19,32,17,8,22,24);(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)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322267);