Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#20275502 |
| Sylow | C53 ⋊ C2×#1953 |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 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)(56,59,60,73,62,75,61,74)(57,64,65,72,66,80,76,86)(58,68,70,83,71,84,69,82)(63,77,78,85,79,87,67,81);(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)(56,58,61,69,62,71,60,70)(57,63,65,78,66,79,76,67)(59,68,74,82,75,84,73,83)(64,77,72,85,80,87,86,81);(56,57,61,65,62,66,60,76)(58,67,69,63,71,78,70,79)(59,72,74,80,75,86,73,64)(68,77,82,85,84,87,83,81);(54,55)1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 173133);