Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×ΓL(1,𝔽8)×D25 |
| unambiguous semidirect product | C25⋊(C2×C7×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D25)⋊(C3×C7) |
| Fitting, Hall | C72×C25 ⋊ C2×C3 |
| derived | C7×C25 ⋊ C2×C3×C7 |
| Hall | C7×ΓL(1,𝔽8)×C25 ⋊ C2 |
| Hall | C72×D25 ⋊ C3 |
| Sylow | C72 ⋊ C3×D25 |
| Sylow | C25 ⋊ C2×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | ΓL(1,𝔽8)×D25 |
| commutator, hypocenter | C7×C25 | C2×C3×C7 |
| Frattini | C5 | C7×D5×ΓL(1,𝔽8) |
| Fitting | C72×C25 | C2×C3 |
| socle | C5×C72 | C3×D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 52);