Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | D53×#2113 |
| Fitting | C53×#2113 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2113 |
1190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
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)(60,68)(64,74)(69,80)(70,81)(75,84)(76,85)(82,88)(86,89);(55,57)(58,60)(59,64)(61,69)(62,70)(63,68)(65,75)(66,76)(67,74)(71,82)(72,80)(73,81)(77,86)(78,84)(79,85)(83,88)(87,89);(54,55)(56,57)(58,59,61,65,62,66,71,77,63,67,72,78,73,79,83,87)(60,64,69,75,70,76,82,86,68,74,80,84,81,85,88,89);(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)1568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322238);