Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#511771 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C24×C3 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C24×C3 ◁ C23×C3×D4 ◁ G | |
11408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
195 conjugacy classes — view the full character table.
| Fitting subgroup of | D3×#511771, #72270758 |
| maximal subgroup of | D3×#511771, C3×#72210575, #72270758, … |
| maximal normal subgroup of | D3×#511771, C3×#72210575, #72270758, … |
Past the SmallGroups library coverage — no SmallGroups id.