Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #88161⋊C3 |
| Fitting | C13×M16 ⋊ C2×C3 |
| Hall | #88161 ⋊ C3 |
| Hall | C13⋊C3 ⋊ #131 |
| Sylow | C13 ⋊ C3×#131 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^3,3,2^2,13|c^2=e,e^2=f,b^a=bf,g^a=g^12,c^b=cf,g^d=g^980 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 384);