Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of D11×D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D45 |
| unambiguous semidirect product | (C5×D11)⋊D9 |
| unambiguous semidirect product | (C9×D11)⋊D5 |
| Fitting, derived, Hall | C5×C9×C11 ⋊ C22 |
| Hall | C9×C11 ⋊ C2×D5 |
| Hall | C5×C11 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D45 |
| Sylow | C9 ⋊ D5×D11 |
| Sylow | C5 ⋊ D9×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C11 | C22 |
| Frattini | C3 | D11×D15 |
| socle | C3×C5×C11 | C2×D3 |
| LCS | G ▷ C5×C9×C11 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 495 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D11×D45, D11×D315, D45×D77, … |
| maximal normal subgroup of | C7×D11×D45, C11×D11×D45, C13×D11×D45, … |
| maximal quotient of | C7×D11×D45, D11×D315, D45×D77, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 25);