Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#5024 |
| Hall | C3×C5 ⋊ #446 |
| Sylow | C3 ⋊ C5×#446 |
188 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 122 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)(6,7,8)(9,11,12,16)(10,13,14,15)(18,21)(22,24);(9,10,12,14)(11,15,16,13);(7,8)(17,18,19,22,20,21,23,24)240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#70895, C5×#68216, #14286639, … |
| maximal normal subgroup of | C5×#70895, C5×#68216, #14286639, … |
| maximal quotient of | C5×#69477, C5×#69478, C5×#69482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4718);