Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C22 |
| direct product | C3×#64902 |
| Fitting | C3×C5×M16 ⋊ 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)(9,11,13,20,14,21,12,19)(10,15,16,23,17,18,22,24);(5,6,7,8)(9,10,12,16,14,17,13,22)(11,18,19,24,21,15,20,23)96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#64902, C3×#10604771, D3×#64902, … |
| maximal normal subgroup of | C2×C3×#64902, C3×#10604771, D3×#64902, … |
| maximal quotient of | C3×#10598556, C3×#10598559, C3×#10598793, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 874);