Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C5⋊D5×C49⋊C3 |
| unambiguous semidirect product | C5⋊(D5×C49⋊C3) |
| Fitting, derived, Hall | C52×C49 ⋊ C2×C3 |
| Hall | C52×C49⋊C3 ⋊ C2 |
| Hall | C49×C5⋊D5 ⋊ C3 |
| Sylow | C49 ⋊ C3×C5⋊D5 |
| Sylow | C52 ⋊ C2×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C49 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)×C5⋊D5 |
| socle | C52×C7 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 19);