Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65294 |
| Fitting | C3×C5×#117 ⋊ C2 |
| Hall | C3×C5 ⋊ #421 |
| Sylow | C5 ⋊ C3×#421 |
308 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 118 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)(10,15,16,17)(11,18)(14,21,22,23)(19,24);(9,11)(10,14)(12,19)(13,18)(15,23)(16,22)(17,21)(20,24);(5,6)(7,8)(9,10)(11,14)(12,15)(13,16)(17,20)(18,22)(19,23)(21,24)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601088, C3×#10600847, #14297300, … |
| maximal normal subgroup of | C3×#10601088, C3×#10600847, #14297300, … |
| maximal quotient of | C3×#10601548, C3×#10601550, C3×#10601560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4097);