Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#20276419 |
| Fitting | C2×C53×#357 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2138 |
1190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 91 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)(60,63,66,65)(61,68,70,80)(62,72,74,81)(64,75,79,78)(67,82,84,83)(69,76,86,90)(71,87,88,85)(73,77,89,91);(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)(60,62)(61,67)(63,72)(64,77)(65,81)(66,74)(68,82)(69,85)(70,84)(71,76)(73,78)(75,89)(79,91)(80,83)(86,87)(88,90);(56,57,58,59)(60,61)(62,71)(63,68)(64,76)(65,80)(66,70)(67,73)(69,78)(72,87)(74,88)(75,86)(77,82)(79,90)(81,85)(83,91)(84,89);(54,55)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322447);