Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×AGL(1,ℤ/32) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #12067 |
| commutator | C16 | C22×C3×C8 |
| Frattini, cosocle | #346 | C23×C3 |
| prime radical | C3×#2263 | C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ C3×#1313 ◁ G | |
276 conjugacy classes of subgroups.
141 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.