Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C13×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C13 ⋊ #21005 |
1782 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^8,13|a^2=g,b^2=eg,d^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^5,d^b=dh,e^b=eh,f^b=fh,g^b=gh,i^b=i^8,e^c=eh,f^c=fh,g^c=gh,i^g=i^12124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1105329);