Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33×C5 · Schur multiplier (H2) = C22×C33 |
| direct product | C22×C32×C5×A4 |
| Fitting, socle | C24×C32×C5 ⋊ C3 |
| derived | C22 ⋊ C22×C33×C5 |
| Hall | C24×C5 ⋊ C33 |
| Sylow | C24 ⋊ C33×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32×C5 | A4 |
| commutator, cosocle, hypocenter | C22 | C22×C33×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32×C5 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C22×C32×C5 | |
788 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 340 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C32×C5×S4 |
| maximal normal subgroup of | C22×C32×C5×S4 |
Past the SmallGroups library coverage — no SmallGroups id.