Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C29 |
| direct product | C3×#493370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C22×#99 |
| commutator | C22×C4 | C23×C3×C4 |
| Frattini, cosocle | C22×D4 | C24×C3 |
| prime radical | C22×C3×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C25×C3 ◁ C24×C3×D4 ◁ G | |
8524 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
204 conjugacy classes — view the full character table.
| Fitting subgroup of | D3×#493370, #72253559, #72253715, … |
| maximal subgroup of | C3×#72210462, D3×#493370, #72253559, … |
| maximal normal subgroup of | C3×#72210462, D3×#493370, #72253559, … |
Past the SmallGroups library coverage — no SmallGroups id.