Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | D73⋊#2957 |
| Fitting | C2×#135×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#2957 |
2642 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,c^2=g,f^2=h,g^2=h,b^a=bf,d^a=dh,f^a=fh,i^a=i^46,f^b=fh,d^c=dh,i^c=i^27,i^e=i^72,i^g=i^72592 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1115041);