Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
| unambiguous semidirect product | D73⋊#2128 |
| Fitting | #535×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#2128 |
1422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=f,c^2=h,e^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^27,c^b=ch,e^b=eh,f^b=fgh,i^d=i^72,f^e=fh,i^f=i^72442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1113518);