Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D33×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C5×D33) |
| unambiguous semidirect product | (C3×AGL(1,𝔽11))⋊D11 |
| unambiguous semidirect product | (C11×AGL(1,𝔽11))⋊D3 |
| Fitting, socle, derived, Hall | C3×C112 ⋊ C22×C5 |
| Hall | C3×C11×C11⋊C5 ⋊ C22 |
| Hall | D11×D33 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ C2×D3 |
| Sylow | C112 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ D11×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C112 | C22×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 118);