Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×D3×S4 |
| Fitting, socle | C22×C32×C5 ⋊ C2×D3 |
| derived | C3×A4 ⋊ C22×C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D3×S4 |
| commutator, cosocle, hypocenter | C3×A4 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C5 | C2×D3 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C3×C5 | |
326 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×S4×AGL(1,ℤ/9), C3×D3×D5×S4 |
| maximal normal subgroup of | C3×D3×D5×S4 |
| maximal quotient of | C5×S4×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id.