Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D7×AΓL(1,𝔽8) |
| Fitting, socle | C23×C7 ⋊ C2×ΓL(1,𝔽8) |
| derived | C7×AGL(1,𝔽8) ⋊ C2×C3 |
| Hall | D7×AGL(1,𝔽8) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×AGL(1,𝔽8) | C2×C3 |
| Fitting, socle | C23×C7 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C7×AGL(1,𝔽8) | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
40 conjugacy classes — view the full character table.
| maximal subgroup of | D7×AGL(3,𝔽2), AGL(1,𝔽7)×AΓL(1,𝔽8) |
| maximal normal subgroup of | AGL(1,𝔽7)×AΓL(1,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.