Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D3×C25 |
| unambiguous semidirect product | C3⋊(C22×C3×C25) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C3×C25) |
| Fitting | C2×C32×C25 ⋊ C2 |
| derived | C3 ⋊ C22×C3×C25 |
| Hall | C32×C25 ⋊ C22 |
| Sylow | C32 ⋊ C22×C25 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×Dic25, C3×#10597031, C3×#10597032, … |
| maximal normal subgroup of | C3×D3×Dic25, C3×#10597031, C3×#10597032, … |
| maximal quotient of | C3×Dic6×C25, C3×C4×D3×C25, C3×D12×C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 41);