Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×#6045⋊C3 |
| unambiguous semidirect product | #6045⋊C32 |
| unambiguous semidirect product | (C3×#6045)⋊C3 |
| Hall | C3×C52⋊C3 ⋊ Q8 |
| Hall | #6045 ⋊ C32 |
| Sylow | C52 ⋊ C32×Q8 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 375);