Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C2 |
| direct product | D3×Dic3×C25 |
| unambiguous semidirect product | (C3×D3)⋊(C4×C25) |
| derived, Sylow | C32 ⋊ C2×C4×C25 |
| Hall | C32×C25 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D32 |
| commutator, hypocenter | C32 | C2×C4×C25 |
| Frattini | C2×C5 | C5×D32 |
| Fitting | C2×C32×C25 | C22 |
| socle, cosocle | C2×C32×C5 | C22×C5 |
| prime radical | C2×C3×C5×D3 | C2×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C25 | |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 80);