Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C73×AGL(1,ℤ/16) ⋊ C2 |
| Sylow | C73 ⋊ #33688 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|d^2=e,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,f^b=fh,i^b=i^72,d^c=dg,e^c=eh,f^c=fg,g^c=gh,f^d=fh862 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 324798);