Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of D9×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D9×D11 |
| Fitting, Hall | C5×C9×C11 ⋊ C22 |
| derived, Hall | C9×C11 ⋊ C22×C5 |
| Hall | C5×C11 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C2×C5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D9×D11 |
| commutator, cosocle, hypocenter | C9×C11 | C22×C5 |
| Frattini | C3 | C5×D3×D11 |
| Fitting | C5×C9×C11 | C22 |
| socle | C3×C5×C11 | C2×D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 495 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7×D9×D11, C5×D11×D63, C5×D9×D77, … |
| maximal normal subgroup of | C5×C7×D9×D11, C5×C11×D9×D11, C5×C13×D9×D11, … |
| maximal quotient of | C5×C7×D9×D11, C5×D11×D63, C5×D9×D77, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 24);