Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C5 · Schur multiplier (H2) = C22×C33 |
| direct product | C3×C5×A42 |
| Fitting, socle | C24×C3×C5 ⋊ C32 |
| derived, Sylow | C24 ⋊ C33×C5 |
| Hall | C24×C5 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | A42 |
| commutator, cosocle, hypocenter | C24 | C33×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C5 | C32 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C3×C5 | |
316 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×A42, C3×C5×A4⋊S4, C3×C5⋊(A4⋊S4) |
| maximal normal subgroup of | C3×D5×A42, C3×C5×A4⋊S4, C3×C5⋊(A4⋊S4) |
| maximal quotient of | C5×#13049240 |
Past the SmallGroups library coverage — no SmallGroups id.