Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D11×D55 |
| unambiguous semidirect product | (C5×D11)⋊(C3×D11) |
| unambiguous semidirect product | (C11×D11)⋊(C3×D5) |
| Fitting, socle, Hall | C3×C5×C112 ⋊ C22 |
| derived, Hall | C5×C112 ⋊ C22×C3 |
| Hall | C3×C112 ⋊ C2×D5 |
| Sylow | C112 ⋊ C2×C3×D5 |
| Hall | C3×C5 ⋊ D112 |
| Sylow | C5 ⋊ C3×D112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×D55 |
| commutator, hypocenter | C5×C112 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C22 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
609 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D11×D55, C3×#10624391⋊D5, C32×D11×D55, … |
| maximal normal subgroup of | C9×D11×D55, C32×D11×D55, C3×D11×C5⋊AGL(1,𝔽11), … |
| maximal quotient of | C9×D11×D55, C32×D11×D55, C3×D11×D165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 191);