Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C28 |
| direct product | C3×#404015 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #2404 |
| commutator, Frattini, cosocle | C25 | C24×C3 |
| LCS | G ▷ C25 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C25×C3 ◁ G | |
6766 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
204 conjugacy classes — view the full character table.
| Fitting subgroup of | #72270253, D3×#404015, #72271352 |
| maximal subgroup of | #72270253, C3×#72219157, D3×#404015, … |
| maximal normal subgroup of | #72270253, C3×#72219157, D3×#404015, … |
Past the SmallGroups library coverage — no SmallGroups id.