Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#20276451 |
| Sylow | C53 ⋊ C2×#2145 |
1170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 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)(56,59,61,73)(57,63,66,65)(58,68,70,71)(60,72,76,85)(62,77,78,82)(64,79,81,74)(67,83,84,80)(69,75,86,87);(56,58)(57,62)(59,68)(60,75)(61,70)(63,77)(64,80)(65,82)(66,78)(67,79)(69,85)(71,73)(72,86)(74,84)(76,87)(81,83);(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)(56,57)(58,67,70,84)(59,63)(60,74)(61,66)(62,69,78,86)(64,72)(65,73)(68,83,71,80)(75,82,87,77)(76,79)(81,85);(54,55)1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322510);