Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#20276945 |
| Sylow | C53 ⋊ C2×#2242 |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 95 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(57,61)(60,63)(64,67,68,83,87,80,69,82,71,85,88,81,70,84,79,66)(65,73,74,92,90,95,75,72,77,78,89,94,76,91,86,93);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,58,59,62)(57,60,61,63)(64,66,79,84,70,81,88,85,71,82,69,80,87,83,68,67)(65,72,86,95,76,92,89,73,77,93,75,91,90,94,74,78);(56,57)(58,60)(59,61)(62,63)(64,65)(66,78)(67,72)(68,86)(69,89)(70,90)(71,77)(73,82)(74,79)(75,88)(76,87)(80,92)(81,91)(83,95)(84,94)(85,93);(54,55)1220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324860);