Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic26⋊A4 |
| unambiguous semidirect product | (C22⋊(C13⋊C3))⋊Q8 |
| Hall | C22×Dic26 ⋊ C3 |
| Sylow | C13 ⋊ Q8×A4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^2,3,2^3,13|a^2=d,b^2=d,b^a=bd,g^a=g^12,e^c=ef,f^c=e,g^c=g^352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1268);