Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#64939 |
| Hall | C3×C5 ⋊ #382 |
| Sylow | C5 ⋊ C3×#382 |
308 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,10,11,12)(13,14)(15,16)(18,22)(21,24);(13,14,15,16)(17,19,20,23)(18,21,22,24);(5,6)(7,8)(13,14,15,16)(17,18)(19,21)(20,22)(23,24)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598508, #14276964, C3×#10599073, … |
| maximal normal subgroup of | C3×#10598508, #14276964, C3×#10599073, … |
| maximal quotient of | C3×#10600195, C3×#10600194, C3×#10600197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3742);