Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #88113⋊C3 |
| Hall | #88113 ⋊ C3 |
| Hall | C13⋊C3 ⋊ #101 |
| Sylow | C13 ⋊ C3×#101 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^2,3,2^3,13|a^2=d,b^2=f,d^2=f,b^a=be,e^a=ef,g^a=g^8,d^b=df,g^c=g^3,g^d=g^1241 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 297);