Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×#64748 |
| Hall | C3×C5 ⋊ #324 |
| Sylow | C5 ⋊ C3×#324 |
156 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 156 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) = 480 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(17,19,20,24)(18,21,22,23);(5,6)(7,8)(9,10,11,13,12,14,15,16)(17,18)(19,23,24,21)(20,22)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10597945, C3×#10598131, #14277587, … |
| maximal normal subgroup of | C3×#10597945, C3×#10598131, #14277587, … |
| maximal quotient of | C3×#10598129, C3×#10598104, C3×#10598200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 300);