Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| unambiguous semidirect product | D73⋊#1747 |
| Fitting | #405×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#1747 |
930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=e,e^2=h,b^a=be,g^a=gh,i^a=i^27,f^b=fh,i^d=i^72,i^f=i^72808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1103511);