Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C5 |
| direct product | C2×#6045⋊C3 |
| unambiguous semidirect product | (C2×#6045)⋊C3 |
| Hall | C2×#6045 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C2×Q8 |
| Sylow | C52 ⋊ C2×C3×Q8 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 683);