Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D53×#2191 |
| Fitting | C53×#2191 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2191 |
1128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(4,17)(8,27)(11,29)(12,22)(15,31)(16,32)(19,25)(26,30)(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)(4,16)(5,21)(6,13)(8,26)(9,28)(10,23)(11,15)(12,19)(14,18)(17,32)(20,24)(22,25)(27,30)(29,31);(1,2,6,10)(3,11,13,29)(4,15,17,31)(5,20,18,9)(7,22,23,12)(8,25,27,19)(14,30,21,26)(16,28,32,24);(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)560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323455);