Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | D7×GL(3,𝔽2) |
| Fitting | C7 ⋊ C2×GL(3,𝔽2) |
| socle, derived | C7×GL(3,𝔽2) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C7×GL(3,𝔽2) | C2 |
| Fitting, cosocle | C7 | C2×GL(3,𝔽2) |
| LCS | G ▷ C7×GL(3,𝔽2) | |
| UCS | C1 | |
81 conjugacy classes of subgroups.
30 conjugacy classes — view the full character table.
| maximal subgroup of | D7×AGL(3,𝔽2), AGL(1,𝔽7)×GL(3,𝔽2) |
| maximal normal subgroup of | AGL(1,𝔽7)×GL(3,𝔽2) |
| maximal quotient of | D7×AGL(3,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.