Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | D53×#2153 |
| Fitting | C53×#2153 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2153 |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(3,13)(8,22)(12,26)(14,16)(15,28)(21,29)(23,31)(27,32)(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);(1,3,4,14,7,13,6,16)(2,8,9,12,11,22,17,26)(5,15,18,21,20,28,19,29)(10,23,24,27,25,31,30,32);(1,2,5,10,6,9,19,24,7,11,20,25,4,17,18,30)(3,12,15,27,16,22,29,31,13,26,28,32,14,8,21,23);(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, 322565);