Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#20276962 |
| Sylow | C53 ⋊ C2×#2245 |
582 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2)(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)(57,61)(60,63)(64,67,68,82,84,94,78,81,71,83,85,80,70,79,69,66)(65,73,74,91,86,95,87,90,77,92,93,89,76,88,75,72);(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)(56,58,59,62)(57,60,61,63)(64,66,78,94,70,80,68,67,71,81,69,79,84,82,85,83)(65,72,87,95,76,89,74,73,77,90,75,88,86,91,93,92);(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)(58,60)(59,61)(62,63)(64,65,71,77)(66,73,81,92)(67,72,83,90)(68,75,85,87)(69,74,78,93)(70,86,84,76)(79,91,94,89)(80,95,82,88);(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, 324887);