Finite Group DatabasebetaFinite Group Databasebeta| order | 2688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | AGL(1,𝔽7)×#550 |
| Fitting | C7×#550 ⋊ C2×C3 |
| Hall | D7×#550 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#550 |
| Sylow | C7 ⋊ C2×C3×#550 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×AGL(1,𝔽7) |
| commutator, socle, cosocle | C22×C7 | C25×C3 |
| Fitting | C7×#550 | C2×C3 |
| hypercenter | #550 | AGL(1,𝔽7) |
| hypocenter | C7 | C2×C3×#550 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #550 | |
3472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#3498 |
| maximal normal subgroup of | AGL(1,𝔽7)×#3498 |
Past the SmallGroups library coverage — no SmallGroups id.