Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C22 |
| direct product | C3×#64894 |
| Fitting | C2×C3×C5×C8 ⋊ C4 |
| Hall | C3×C5 ⋊ #344 |
| Sylow | C5 ⋊ C3×#344 |
180 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 2 generators on 24 points:
(1,2,3)(4,5,6,8,7)(9,11,12,19,13,18,20,24)(10,14,15,21,16,17,22,23);(5,6,7,8)(9,10)(11,17,18,14)(12,15)(13,16)(19,23,24,21)(20,22)114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#64894, C3×#10604763, D3×#64894, … |
| maximal normal subgroup of | C2×C3×#64894, C3×#10604763, D3×#64894, … |
| maximal quotient of | C3×#10598774, C3×#10598766, C3×#10598775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 866);