Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C3×#6512843 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C22×#120 |
| commutator, Frattini, cosocle | C24 | C25×C3 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C24×C3×C4 ◁ G | |
10120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
240 conjugacy classes — view the full character table.
| Fitting subgroup of | D3×#6512843, #72271268 |
| maximal subgroup of | D3×#6512843, #72271268 |
| maximal normal subgroup of | D3×#6512843, #72271268 |
Past the SmallGroups library coverage — no SmallGroups id.