Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#489347 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #18524 |
| commutator, Frattini, cosocle | C4×C8 | C24×C3 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×C4×M16 ◁ G | |
1920 conjugacy classes of subgroups.
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#489347, C3×#72215247 |
| maximal normal subgroup of | D3×#489347 |
| maximal quotient of | C3×#72215247 |
Past the SmallGroups library coverage — no SmallGroups id.