Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D11×D33 |
| Fitting, socle, Hall | C3×C5×C112 ⋊ C22 |
| derived, Hall | C3×C112 ⋊ C22×C5 |
| Hall | C5×C112 ⋊ C2×D3 |
| Sylow | C112 ⋊ C2×C5×D3 |
| Hall | C3×C5 ⋊ D112 |
| Sylow | C3 ⋊ C5×D112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D11×D33 |
| commutator, hypocenter | C3×C112 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C22 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups.
630 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D11×D99, C5×#10624391⋊D3, C3×C5×D11×D33, … |
| maximal normal subgroup of | C3×C5×D11×D33, #20258405⋊D3, #20258406⋊D3, … |
| maximal quotient of | C5×D11×D99, C3×C5×D11×D33, C5×D332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 196);