Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×#11760386 |
| Fitting, socle, Hall | C52×C72 ⋊ C2×C3 |
| derived | C52×C7 ⋊ C2×C3×C7 |
| Hall | C7×C7⋊(C52⋊C3) ⋊ C2 |
| Hall | C7×C5⋊D35 ⋊ C3 |
| Sylow | C72 ⋊ (C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11760386 |
| commutator, hypocenter | C52×C7 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | C2×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C7 | |
56 conjugacy classes of subgroups.
245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 111);