Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C5 |
| direct product | Q8×C52⋊C9 |
| Hall | C52×Q8 ⋊ C9 |
| Sylow | C52 ⋊ Q8×C9 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 184);