Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#16810896 |
| Sylow | C53 ⋊ C4×#473 |
882 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 points:
(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)(58,61)(59,66)(60,71)(62,76)(63,78)(64,77)(65,79)(67,75)(68,83)(69,82)(70,84)(72,86)(73,88)(74,87)(80,89)(81,85);(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)(58,60,63,73,64,74,62,72)(59,65,68,80,69,81,67,70)(61,71,78,88,77,87,76,86)(66,79,83,89,82,85,75,84);(58,59,64,69)(60,70,74,80)(61,75,77,83)(62,68,63,67)(65,73,81,72)(66,78,82,76)(71,85,87,79)(84,88,89,86);(54,55,56,57)1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 176455);