Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D5×C11×D33 |
| unambiguous semidirect product | (C3×D5)⋊(C11×D11) |
| unambiguous semidirect product | (D5×C11)⋊(D3×C11) |
| Fitting, socle, Hall | C3×C5×C112 ⋊ C22 |
| derived | C3×C5×C11 ⋊ C22×C11 |
| Hall | C5×C112 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D5 |
| Sylow | C112 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×C11×D11 |
| Sylow | C5 ⋊ C2×C11×D33 |
| Sylow | C3 ⋊ D5×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D5×D33 |
| commutator, hypocenter | C3×C5×C11 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C22 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 ◁ C11 | |
120 conjugacy classes of subgroups.
792 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 209);