Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65197 |
| Fitting | C3×C5×M32 ⋊ C2 |
| Hall | C3×C5 ⋊ #509 |
| Sylow | C5 ⋊ C3×#509 |
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 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)(9,10,16,22,12,17,19,20,13,15,23,24,18,21,11,14);(10,15)(14,20)(17,21)(22,24);(5,6)(7,8)(10,14)(11,16)(12,18)(15,20)(17,24)(19,23)(21,22)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10600103, C3×#10599884, #14315900, … |
| maximal normal subgroup of | C3×#10600103, C3×#10599884, #14315900, … |
| maximal quotient of | C3×#10602232, C3×#10602233, C3×#10602221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4000);