Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#20275631 |
| Sylow | C53 ⋊ C2×#1979 |
1438 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 91 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)(60,63,65,76,66,77,64,75)(61,68,78,88,69,84,70,74)(62,71,79,89,72,86,73,87)(67,80,82,90,83,91,81,85);(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)(56,58,59,57)(60,62,64,73,66,72,65,79)(61,67,70,81,69,83,78,82)(63,71,75,87,77,86,76,89)(68,80,74,85,84,91,88,90);(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)(56,57,59,58)(60,61,65,70,66,69,64,78)(62,67,73,82,72,83,79,81)(63,74,76,84,77,88,75,68)(71,85,87,80,86,90,89,91);(54,55)1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 173569);