Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×Dic50 |
| unambiguous semidirect product | (D3×C25)⋊Q8 |
| Hall | C3×C25 ⋊ C2×Q8 |
| Sylow | C25 ⋊ D3×Q8 |
| Sylow | C3 ⋊ C2×Dic50 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 125);