Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C9 · Schur multiplier (H2) = C22×C3 |
| direct product | C5×(C22⋊A4)⋊C9 |
| derived, Sylow | C24 ⋊ C3×C5×C9 |
| Hall | C24×C5 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | A42 |
| commutator, hypocenter | C24 | C3×C5×C9 |
| Frattini | C3 | C5×A42 |
| Fitting, socle | C24×C3×C5 | C32 |
| prime radical | C3×C5×C22⋊A4 | C3 |
| cosocle | C24×C3 | C32×C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C3×C5 | |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
240 conjugacy classes — view the full character table.
| derived subgroup of | #72254690, #72269593, D5×#11724027 |
| maximal subgroup of | D5×(C22⋊A4)⋊C9, C5×#13049240, C5×#11724027, … |
| maximal normal subgroup of | D5×(C22⋊A4)⋊C9, C5×#13049240, C5×#11724027, … |
Past the SmallGroups library coverage — no SmallGroups id.