Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×C3×#8534 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | #379 |
| commutator | C24 | C23×C3×C4 |
| Frattini, cosocle | C25 | C24×C3 |
| prime radical | C2×C3×#3484 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ C26×C3 ◁ G | |
9744 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
240 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#72231371, C2×D3×#8534, #72270349, … |
| maximal subgroup of | C2×#72231371, C2×D3×#8534, C2×C3×#347042, … |
| maximal normal subgroup of | C2×#72231371, C2×D3×#8534, C2×C3×#347042, … |
Past the SmallGroups library coverage — no SmallGroups id.