Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D3×D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×Dic75 |
| unambiguous semidirect product | (C3×D3)⋊Dic25 |
| derived, Hall | C32×C25 ⋊ C2×C4 |
| Sylow | C25 ⋊ D3×Dic3 |
| Sylow | C32 ⋊ C2×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D75 |
| commutator, hypocenter | C32×C25 | C2×C4 |
| Frattini | C2×C5 | D3×D15 |
| Fitting, cosocle | C2×C32×C25 | C22 |
| socle | C2×C32×C5 | C2×D5 |
| prime radical | C2×C3×C5×D3 | D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C2 | |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 89);