Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4777 |
| Fitting | C3×C5×#102 ⋊ C2 |
| Hall | C3×C5 ⋊ #481 |
| Sylow | C3 ⋊ C5×#481 |
228 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(10,14)(13,16)(18,21)(20,24)(22,23);(9,11,12,15)(10,13,14,16)(17,18,19,22)(20,21,24,23);(7,8)(9,10)(11,13)(12,14)(15,16)165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#481, C2×C5×#4777, D5×#4777, … |
| maximal normal subgroup of | C5×D3×#481, C2×C5×#4777, D5×#4777, … |
| maximal quotient of | C5×#68872, C5×#68875, C5×#70200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4471);