Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C211 |
| direct product | C3×#6437445 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C22×#120 |
| commutator, Frattini, cosocle | C22×C4 | C25×C3 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C24×C3×C4 ◁ G | |
14180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
240 conjugacy classes — view the full character table.
| Fitting subgroup of | #72253696, #72253711, #72270085, … |
| maximal subgroup of | C3×#72210479, #72253696, #72253711, … |
| maximal normal subgroup of | C3×#72210479, #72253696, #72253711, … |
Past the SmallGroups library coverage — no SmallGroups id.