Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D3×#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×#1035 |
| unambiguous semidirect product | (C3×#1035)⋊(C2×C3) |
| unambiguous semidirect product | (C3⋊#1035)⋊(C2×C3) |
| Fitting, Hall | C32×C25 ⋊ C2×C4 |
| derived | C3×C25 ⋊ C2×C3×C4 |
| Sylow | C25 ⋊ C3×C4×D3 |
| Sylow | C32 ⋊ C2×#1035 |
105 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 105 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 150 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#1035, C3×D3×AGL(1,ℤ/25), AGL(1,ℤ/9)×#1035 |
| maximal normal subgroup of | D32×#1035, C3×D3×AGL(1,ℤ/25) |
| maximal quotient of | AGL(1,ℤ/9)×#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 218);