Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#20276598 |
| Fitting | C2×C53×#359 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2179 |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 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)(56,59,61,74,62,75,78,60)(57,64,66,76,68,65,67,83)(58,70,71,79,73,87,72,77)(63,80,81,69,82,84,85,86);(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)(57,63)(59,70)(60,77)(61,71)(62,73)(64,80)(65,84)(66,81)(67,85)(68,82)(69,76)(72,78)(74,79)(75,87)(83,86);(56,57,61,66,62,68,78,67)(58,69,71,84,73,86,72,80)(59,65,74,83,75,64,60,76)(63,79,81,87,82,77,85,70);(54,55)1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322971);