Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20274042 |
| Sylow | C53 ⋊ C2×#1663 |
830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 13568 |
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)(57,61)(59,68)(60,65)(62,71)(63,70)(64,66)(67,69)(72,75,77,73)(74,81,83,78)(76,79,86,84)(80,85,87,82);(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)(56,57,60,63)(58,61,65,70)(59,67,66,62)(64,71,68,69)(72,74,77,83)(73,78,75,81)(76,85,86,82)(79,87,84,80);(58,64)(59,66)(61,69)(62,67)(65,68)(70,71)(72,73,77,75)(74,80,83,87)(76,84,86,79)(78,85,81,82);(54,55)872 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150757);