Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65494 |
| Fitting | C3×C5×#137 ⋊ C2 |
| Hall | C3×C5 ⋊ #456 |
| Sylow | C5 ⋊ C3×#456 |
284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 78 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 — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,12,15,16)(10,17,19,24)(11,20,21,18)(13,23,14,22);(9,11,15,21)(10,16,19,12)(13,17,14,24)(18,23,20,22);(5,6)(7,8)(9,10)(11,16)(12,21)(13,20)(14,18)(15,19)(17,22)(23,24)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#456, C2×C3×#65494, #14425144, … |
| maximal normal subgroup of | C3×D5×#456, C2×C3×#65494, #14425144, … |
| maximal quotient of | C3×#10601767, C3×#10601775, C3×#10601768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4297);