Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#20275773 |
| Fitting | C22×#137×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2009 |
1926 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)(56,59,62,75)(57,64,67,81)(58,69,71,85)(60,74,61,73)(63,77,78,79)(65,72,66,80)(68,83,82,87)(70,86,76,84);(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)(56,58)(57,63)(59,69)(60,76)(61,70)(62,71)(64,79)(65,82)(66,68)(67,78)(72,83)(73,86)(74,84)(75,85)(77,81)(80,87);(56,57)(58,68)(59,72)(60,66)(61,65)(62,67)(63,70)(64,74)(69,77)(71,82)(73,81)(75,80)(76,78)(79,85)(83,84)(86,87);(54,55)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 196567);