Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#20275981 |
| Sylow | C53 ⋊ C2×#2047 |
1330 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)(57,59)(60,63,64,76,65,77,80,91)(61,67,68,84,69,74,78,89)(62,71,72,88,73,75,79,90)(66,81,70,86,82,83,85,87);(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)(60,62,65,73)(61,66,69,82)(63,75,77,71)(64,79,80,72)(67,83,74,81)(68,85,78,70)(76,88,91,90)(84,86,89,87);(56,57)(58,59)(60,61,65,69)(62,70,73,85)(63,74,77,67)(64,78,80,68)(66,79,82,72)(71,87,75,86)(76,84,91,89)(81,88,83,90);(54,55)1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 197364);