Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| direct product | A4×SL(2,𝔽8) |
| Fitting | C22 ⋊ C3×SL(2,𝔽8) |
| socle, derived | C22×SL(2,𝔽8) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C22×SL(2,𝔽8) | C3 |
| Fitting, cosocle | C22 | C3×SL(2,𝔽8) |
| LCS | G ▷ C22×SL(2,𝔽8) | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
36 conjugacy classes — view the full character table.
| maximal subgroup of | A5×SL(2,𝔽8) |
| maximal quotient of | SL(2,𝔽3)×SL(2,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.