Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#6122⋊C3 |
| unambiguous semidirect product | (C2×#6122)⋊C3 |
| Hall | C2×#6122 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×M16 |
| Sylow | C13 ⋊ C2×C3×M16 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1166);