Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65532 |
| Hall | C3×C5 ⋊ #458 |
| Sylow | C5 ⋊ C3×#458 |
320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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)(10,15)(11,17)(13,19)(14,20)(16,22)(18,24)(21,23);(9,11)(10,14)(12,17)(13,18)(15,20)(16,21)(19,24)(22,23);(5,6)(7,8)(9,10,13,16)(11,14,18,21)(12,15,19,22)(17,23,24,20)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601791, C3×#10601783, #14316690, … |
| maximal normal subgroup of | C3×#10601791, C3×#10601783, #14316690, … |
| maximal quotient of | C3×#10602636, C3×#10602683, C3×#10602679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4335);