Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#352×C73 ⋊ C2 |
| Sylow | C73 ⋊ #12754 |
782 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,c^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^72,e^b=egh,f^b=fg,i^b=i^72,d^c=dg,e^d=eh,f^d=fh970 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 85336);