Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| unambiguous semidirect product | D73⋊#3573 |
| Sylow | C73 ⋊ C2×#3573 |
10858 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,g^2=h,i^a=i^27,e^b=eh,d^c=dh,i^f=i^72,i^g=i^72748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116303);