Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D53×#2097 |
| Fitting | C53×#2097 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2097 |
1150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 81 points:
(2,4)(13,15,17,24)(14,19,21,27)(16,26,25,23)(18,22,20,28)(29,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31);(1,2)(3,4)(5,7,8,12)(6,9,10,11)(14,18)(16,25)(19,22)(20,21)(23,26)(27,28);(5,6,8,10)(7,11,12,9)(13,14,16,20,17,21,25,18)(15,22,23,27,24,28,26,19);(30,31)(32,33)(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)896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 199353);