Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#20276677 |
| Fitting | C2×C53×#472 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2193 |
1098 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)(56,58,62,69)(57,64,66,81)(59,68,73,84)(60,74,61,67)(63,76,77,87)(65,80,75,79)(70,83,72,86)(71,85,82,78);(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)(56,57)(58,64)(59,71)(60,65)(61,75)(62,66)(63,70)(67,79)(68,85)(69,81)(72,77)(73,82)(74,80)(76,83)(78,84)(86,87);(57,63)(58,67)(59,70)(60,61)(64,78)(65,82)(66,77)(68,84)(69,74)(71,75)(72,73)(76,79)(80,87)(81,85);(54,55)878 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323505);