Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of D3×D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×D33 |
| unambiguous semidirect product | (C3×D3)⋊(C5×D11) |
| Fitting, socle, Hall | C32×C5×C11 ⋊ C22 |
| derived, Hall | C32×C11 ⋊ C22×C5 |
| Hall | C5×C11 ⋊ D32 |
| Hall | C32×C5 ⋊ C2×D11 |
| Sylow | C11 ⋊ C5×D32 |
| Sylow | C32 ⋊ C2×C5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×D33 |
| commutator, cosocle, hypocenter | C32×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C11 | C22 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C5 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 330 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C7×D33, C5×D3×D231, C5×D21×D33, … |
| maximal normal subgroup of | C5×D3×C7×D33, C5×D3×C11×D33, C5×D3×C13×D33, … |
| maximal quotient of | C5×D3×C7×D33, C5×D3×D231, C5×D21×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 99);