Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D53×#1814 |
| Fitting | C53×#1814 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1814 |
1330 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)(2,9)(3,13)(5,18)(6,21)(7,19)(8,22)(10,24)(11,25)(12,26)(14,28)(15,30)(16,29)(17,20)(23,32)(27,31)(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);(1,3,5,14,7,16,6,15)(2,8,10,12,11,23,20,27)(4,13,18,28,19,29,21,30)(9,22,24,26,25,32,17,31);(1,2)(3,12)(4,17,19,24)(5,20)(6,10)(7,11)(8,14)(9,18,25,21)(13,22,29,32)(15,23)(16,27)(26,28,31,30);(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, 169226);