Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#10597028 |
| derived | C3×C25 ⋊ C2×C3×C4 |
| Hall | C32×C25 ⋊ C2×C4 |
| Sylow | C25 ⋊ C3×C4×D3 |
| Sylow | C32 ⋊ C4×D25 |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 68);