Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65031 |
| Fitting | C3×C5×#99 ⋊ C2 |
| Hall | C3×C5 ⋊ #458 |
| Sylow | C5 ⋊ C3×#458 |
320 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 320 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)(9,12,13,20)(10,15,16,23)(11,17)(14,21)(18,19)(22,24);(9,11)(10,14)(12,19)(13,18)(15,21)(16,22)(17,20)(23,24);(5,6)(7,8)(9,10)(11,14)(12,15)(13,16)(17,24)(18,22)(19,21)(20,23)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599925, C3×#10599946, #14316708, … |
| maximal normal subgroup of | C3×#10599925, C3×#10599946, #14316708, … |
| maximal quotient of | C3×#10599081, C3×#10598903, C3×#10599113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3834);