Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#64762 |
| Hall | C3×C5 ⋊ #355 |
| Sylow | C5 ⋊ C3×#355 |
128 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,14)(12,20)(15,23)(16,17)(18,21)(22,24);(5,6)(7,8)(9,10,11,15,13,17,19,24)(12,16,21,23,20,14,18,22)123 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598263, C3×#10597952, #14279332, … |
| maximal normal subgroup of | C3×#10598263, C3×#10597952, #14279332, … |
| maximal quotient of | C3×#10598131, C3×#10598123, C3×#10598138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 314);