Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| general linear | GL(2,𝔽7) |
| direct product | C3×#10621462 |
| derived | SL(2,𝔽7) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C3 | SO(3,𝔽7) |
| commutator, cosocle, hypocenter | SL(2,𝔽7) | C2×C3 |
| Frattini | C2 | C3×SO(3,𝔽7) |
| LCS | G ▷ SL(2,𝔽7) | |
| UCS | C1 ◁ C2×C3 | |
84 conjugacy classes of subgroups.
48 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.