Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#66056 |
| Hall | C3×C5 ⋊ Q82 |
| Sylow | C5 ⋊ C3×Q82 |
424 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 230 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 — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11)(10,14)(12,16)(13,15)(17,19,20,24)(18,21,22,23);(9,11,12,16)(10,14,15,13)(17,18,20,22)(19,23,24,21);(9,11,12,16)(10,13,15,14);(5,6)(7,8)(9,10,12,15)(11,14,16,13)159 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10602062, C3×#10599297, #14289025, … |
| maximal normal subgroup of | C3×#10602062, C3×#10599297, #14289025, … |
| maximal quotient of | C3×#10606054, C3×#10607712, C3×#10607718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9928);