Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#65263 |
| Hall | C3×C5 ⋊ #391 |
| Sylow | C5 ⋊ C3×#391 |
372 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 166 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)(9,11,12,10)(14,16)(19,23)(21,24);(17,19,20,23)(18,21,22,24);(5,6)(7,8)(9,10,12,11)(13,14,15,16)(17,18,20,22)(19,21,23,24)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598715, #14276683, C3×#10597946, … |
| maximal normal subgroup of | C3×#10598715, #14276683, C3×#10597946, … |
| maximal quotient of | C3×#10602356, C3×#10600198, C3×#10602359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4066);