Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | Q16×D13⋊C3 |
| unambiguous semidirect product | D13⋊(C3×Q16) |
| unambiguous semidirect product | (Q16×D13)⋊C3 |
| Fitting | C13×Q16 ⋊ C2×C3 |
| Hall | Q16×D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×Q16 |
| Sylow | C13 ⋊ C2×C3×Q16 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 394);