Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4 |
| direct product | D53×#2310 |
| Fitting | C53×#2310 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2310 |
5214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 77 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)(63,69)(67,70)(68,77)(75,76);(59,61)(62,65,66,74)(63,68,69,77)(64,71,72,73)(67,75,70,76);(62,64,66,72)(63,67,69,70)(65,73,74,71)(68,76,77,75);(54,55,56,57)(58,59)(60,61)(62,63)(64,70)(65,68)(66,69)(67,72)(71,76)(73,75)(74,77);(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)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 328124);