Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65436 |
| Fitting | C2×C3×C5×D8 ⋊ C2 |
| Hall | C3×C5 ⋊ #509 |
| Sylow | C5 ⋊ C3×#509 |
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,16)(11,13)(12,20)(15,17)(18,24)(19,21)(22,23);(9,11,14,13)(10,15,18,22)(12,19,21,20)(16,23,24,17);(5,6)(7,8)(9,10)(11,15)(12,16)(13,22)(14,18)(17,20)(19,23)(21,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601711, C3×#10600047, #14315888, … |
| maximal normal subgroup of | C3×#10601711, C3×#10600047, #14315888, … |
| maximal quotient of | C3×#10601391, C3×#10602826, C3×#10601389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4239);