Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#689 |
| Hall | C3×C52 ⋊ Q16 |
| Sylow | C52 ⋊ C3×Q16 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 399);