Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×SL(2,𝔽7) |
| derived | C7×SL(2,𝔽7) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×GL(3,𝔽2) |
| commutator, hypocenter | C7×SL(2,𝔽7) | C3 |
| Fitting, socle, cosocle | C2×C7 | C3×GL(3,𝔽2) |
| LCS | G ▷ C7×SL(2,𝔽7) | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
55 conjugacy classes — view the full character table.
| maximal subgroup of | Ω+(4,𝔽7), GL(3,𝔽2)×SL(2,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.