Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×C25) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C25) |
| unambiguous semidirect product | (D7×C25)⋊C3 |
| Fitting, Hall | C7×C25 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C2×C3×C25 |
| Hall | ΓL(1,𝔽8)×C25 ⋊ C2 |
| Hall | D7×C25 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C25 |
| Hall | D7 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | AGL(1,𝔽7) |
| commutator, hypocenter | C7 | C2×C3×C25 |
| Frattini | C5 | C5×AGL(1,𝔽7) |
| Fitting | C7×C25 | C2×C3 |
| socle, cosocle | C5×C7 | C2×C3×C5 |
| prime radical | C5×AGL(1,𝔽7) | C5 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 175 |
175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 1);