Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| isoclinism | isoclinic class of SL(2,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C1 |
| general linear | GL(2,𝔽8) |
| direct product | C7×SL(2,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C7 | SL(2,𝔽8) |
| commutator, hypocenter | SL(2,𝔽8) | C7 |
| Frattini | C1 | G |
| LCS | G ▷ SL(2,𝔽8) | |
| UCS | C1 ◁ C7 | |
33 conjugacy classes of subgroups.
63 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(2,𝔽8) |
| maximal normal subgroup of | ΓL(2,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.