Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | SD32×C13⋊C3 |
| unambiguous semidirect product | (C13×SD32)⋊C3 |
| Fitting, Hall | C13×SD32 ⋊ C3 |
| Sylow | C13 ⋊ C3×SD32 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
77 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 135);