Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| unambiguous semidirect product | D13⋊#1937 |
| Fitting | C13×#416 ⋊ C4 |
| Sylow | C13 ⋊ C2×#1937 |
1114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^8,13|a^2=g,b^2=eg,c^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^5,i^b=i^8,i^d=i^12,i^g=i^12172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1105520);