Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D73⋊#1826 |
| Fitting | C2×#117×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#1826 |
1606 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,c^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^27,f^c=fh,i^d=i^72,i^g=i^72796 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1104662);