Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×#6106⋊C3 |
| unambiguous semidirect product | (C2×#6106)⋊C3 |
| Fitting | C2×Q8×C13 ⋊ C2×C3 |
| Hall | C2×#6106 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×SD16 |
| Sylow | C13 ⋊ C2×C3×SD16 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 420);