Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×#688 |
| unambiguous semidirect product | (C22×#688)⋊C3 |
| Fitting | C22×C5×Q8 ⋊ C2×C3 |
| Hall | C22×#688 ⋊ C3 |
| Sylow | C5 ⋊ A4×SD16 |
166 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#688, #14513319, #14513320, … |
| maximal normal subgroup of | S4×#688, #14513319, #14513320, … |
| maximal quotient of | A4×#3940, A4×#3941, #10615416⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6384);