Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#88881 |
| Hall | C24×C5 ⋊ 3−1+2 |
| Sylow | C24 ⋊ C5×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | A42 |
| commutator, cosocle | C24×C3 | C32×C5 |
| Frattini | C3 | C5×A42 |
| Fitting, socle | C24×C3×C5 | C32 |
| prime radical | C3×C5×C22⋊A4 | C3 |
| hypocenter | C24 | C5×3−1+2 |
| LCS | G ▷ C24×C3 ▷ C24 | |
| UCS | C1 ◁ C3×C5 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#13049240, D5×#88881 |
| maximal normal subgroup of | C5×#13049240, D5×#88881 |
Past the SmallGroups library coverage — no SmallGroups id.