Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×ΓL(1,𝔽8)×C25 |
| unambiguous semidirect product | (C2×C7)⋊(C3×C7×C25) |
| unambiguous semidirect product | (C2×C7×C25)⋊(C3×C7) |
| Fitting, Hall | C2×C72×C25 ⋊ C3 |
| derived | C7 ⋊ C2×C3×C7×C25 |
| Hall | C72×C25 ⋊ C2×C3 |
| Hall | C2×C72 ⋊ C3×C25 |
| Sylow | C72 ⋊ C2×C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C25 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C2×C3×C7×C25 |
| Frattini | C5 | C2×C5×C7×ΓL(1,𝔽8) |
| Fitting | C2×C72×C25 | C3 |
| socle | C2×C5×C72 | C3×C5 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C7×C25 | |
60 conjugacy classes of subgroups.
1750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 61);