Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×A4×M16 |
| unambiguous semidirect product | (C22×M16)⋊(C3×C5) |
| unambiguous semidirect product | (C22×C5×M16)⋊C3 |
| Fitting, Hall | C22×C5×M16 ⋊ C3 |
| Sylow | C22×M16 ⋊ C3×C5 |
166 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#73114, C5×#73115, C5×#73116, … |
| maximal normal subgroup of | C5×#73114, C5×#73115, C5×#73116, … |
| maximal quotient of | C5×A4×#97, C5×A4×C22⋊C8, C5×A4×C4⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9658);