Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20273744 |
| Fitting | C2×C53×#400 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1615 |
1016 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)(57,62)(58,64)(60,66)(61,67)(63,69)(65,71)(68,70)(72,75,77,76)(73,79,80,84)(74,82,83,85)(78,86,87,81);(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)(56,58)(57,61)(59,64)(60,65)(62,67)(63,68)(66,71)(69,70)(72,74)(73,78)(75,82)(76,85)(77,83)(79,86)(80,87)(81,84);(56,57,60,63)(58,61,65,68)(59,62,66,69)(64,70,71,67)(72,73,77,80)(74,81,83,86)(75,79,76,84)(78,85,87,82);(54,55)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 141714);