Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#65689 |
| Fitting | C3×C42×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ #382 |
| Sylow | C5 ⋊ C3×#382 |
308 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,6,8,7)(9,11,12,10)(14,18)(17,20);(9,10,12,11)(13,15,16,19)(14,17,18,20);(5,6,7,8)(10,11)(13,14)(15,17)(16,18)(19,20)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598527, C3×#10598595, #14276977, … |
| maximal normal subgroup of | C3×#10598527, C3×#10598595, #14276977, … |
| maximal quotient of | C3×#10604197, C3×#10604198, C3×#10603802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6417);