Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C210 |
| direct product | C3×#394066 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C2×#120 |
| commutator, Frattini, cosocle | C25 | C24×C3 |
| LCS | G ▷ C25 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ C26×C3 ◁ G | |
12412 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
222 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.