Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×AGL(1,𝔽7)2 |
| Fitting, socle | C22×C72 ⋊ C22×C32 |
| derived, Sylow | C72 ⋊ C24×C32 |
| Hall | C22×D72 ⋊ C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽7)2 |
| commutator, cosocle, hypocenter | C72 | C24×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72 | C22×C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22 | |
1640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
196 conjugacy classes — view the full character table.
| maximal quotient of | #72245383 |
Past the SmallGroups library coverage — no SmallGroups id.