Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #6653 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#6653 |
| Hall | C3×C52 ⋊ D8 |
| Sylow | C52 ⋊ #213 |
| Sylow | C3 ⋊ C5×D40 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 291);