Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #88063⋊C3 |
| Fitting | C13×M16 ⋊ C2×C3 |
| Hall | #88063 ⋊ C3 |
| Hall | C13⋊C3 ⋊ #100 |
| Sylow | C13 ⋊ C3×#100 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2^2,3,2^3,13|b^2=d,d^2=f,b^a=be,d^a=df,g^a=g^12,e^b=ef,g^c=g^353 conjugacy classes — view the full character table.
| maximal subgroup of | #100×D13⋊C3, #72229149, #72259181 |
| maximal normal subgroup of | #100×D13⋊C3, #72229149, #72259181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 34);