Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | D53×#1835 |
| Fitting | C53×#1835 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1835 |
1006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 81 points:
(6,10)(9,12)(13,16,17,25,18,26,24,15)(14,20,21,19,22,23,27,28)(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);(5,7,8,11)(6,9,10,12)(13,15,24,26,18,25,17,16)(14,19,27,20,22,28,21,23);(1,2,3,4)(5,6)(7,9)(8,10)(11,12)(13,14)(15,23)(16,19)(17,27)(18,22)(20,25)(21,24)(26,28);(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)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 169753);