Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×C8×A4 |
| unambiguous semidirect product | (C23×C8)⋊(C3×C5) |
| unambiguous semidirect product | (C23×C5×C8)⋊C3 |
| Fitting, Hall | C23×C5×C8 ⋊ C3 |
| derived | C22 ⋊ C2×C3×C5×C8 |
| Sylow | C23×C8 ⋊ C3×C5 |
186 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
320 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×A4⋊C16, C5×#73104, C5×#73105, … |
| maximal normal subgroup of | C2×C5×A4⋊C16, C5×#73104, C5×#73105, … |
| maximal quotient of | C4×C5×C8×A4, C5×A4×C22⋊C8, C5×A4×C4⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9657);