Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of #64425 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5×C7 |
| direct product | C52×#64425 |
| Fitting, socle, Hall | C52×C72 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C52 |
| Hall | C52×#3862 ⋊ C2 |
| Hall | C52×C7⋊D7 ⋊ C3 |
| Hall | #3862 ⋊ C2×C52 |
| Hall | C7⋊D7 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | #64425 |
| commutator, hypocenter | C72 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C52 | |
160 conjugacy classes of subgroups.
350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 78);