Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| direct product | D3×SL(2,𝔽8) |
| Fitting | C3 ⋊ C2×SL(2,𝔽8) |
| socle, derived | C3×SL(2,𝔽8) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C3×SL(2,𝔽8) | C2 |
| Fitting, cosocle | C3 | C2×SL(2,𝔽8) |
| LCS | G ▷ C3×SL(2,𝔽8) | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
27 conjugacy classes — view the full character table.
| maximal subgroup of | A5×SL(2,𝔽8) |
| maximal quotient of | Dic3×SL(2,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.