Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65428 |
| Fitting | C2×C3×C5×M16 ⋊ 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)(9,11,12,20,14,19,13,22)(10,15,16,24,17,23,21,18);(11,19)(15,23)(18,24)(20,22);(5,6)(7,8)(9,10)(11,18)(12,16)(13,21)(14,17)(15,20)(19,24)(22,23)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601206, C3×#10600803, #14297284, … |
| maximal normal subgroup of | C3×#10601206, C3×#10600803, #14297284, … |
| maximal quotient of | C3×#10601218, C3×#10601549, C3×#10601559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4231);