Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65757 |
| Hall | C3×C5 ⋊ #432 |
| Sylow | C5 ⋊ C3×#432 |
220 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 96 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)(4,5,6,8,7)(9,11,12,15)(10,14,13,16)(18,21)(22,24);(10,13)(14,16);(5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18,19,22,20,21,23,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598697, #14276950, #14276951, … |
| maximal normal subgroup of | C3×#10598697, #14276950, #14276951, … |
| maximal quotient of | C3×#10604175, C3×#10604897, C3×#10604180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6485);