Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D53×#2049 |
| Fitting | C53×#2049 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2049 |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,5,19,7,21,6,20)(2,9,10,26,12,27,11,17)(3,14,15,30,16,18,22,32)(8,23,13,29,24,25,28,31)(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)(2,8)(4,18)(5,22)(6,15)(7,16)(9,25)(10,28)(11,13)(12,24)(14,21)(17,31)(19,30)(20,32)(23,27)(26,29);(1,2,7,12)(3,13,16,28)(4,17,21,26)(5,11,6,10)(8,22,24,15)(9,19,27,20)(14,25,18,23)(29,32,31,30);(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)644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 197402);