Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#20274516 |
| Fitting | C2×C53×#405 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1757 |
1474 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)(56,59,60,70,61,71,72,83)(57,63,64,76,65,77,78,86)(58,67,69,82,68,81,73,84)(62,74,75,85,66,79,80,87);(56,58)(57,62,65,66)(59,67)(60,69)(61,68)(63,74,77,79)(64,75,78,80)(70,82)(71,81)(72,73)(76,85,86,87)(83,84);(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)(56,57,60,64,61,65,72,78)(58,66,69,80,68,62,73,75)(59,63,70,76,71,77,83,86)(67,79,82,87,81,74,84,85);(54,55)2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 167267);