Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C2×C3×#33553 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C25×C3 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×#41 ◁ G | |
8414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
204 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×D3×#33553, #72269887 |
| maximal subgroup of | C3×#72215601, C2×D3×#33553, #72269887 |
| maximal normal subgroup of | C3×#72215601, C2×D3×#33553, #72269887 |
Past the SmallGroups library coverage — no SmallGroups id.