Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #131⋊(C13⋊C3) |
| Fitting, Hall | C13×#131 ⋊ C3 |
| Sylow | #131 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ #131⋊C3 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2,3,2^3,13,2|a^2=c,c^2=g,d^2=g,e^2=g,d^b=de,e^b=d,f^b=f^3,e^d=eg108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 869);