Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D73⋊#1308 |
| Sylow | C73 ⋊ C2×#1308 |
526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,e^2=gh,f^2=g,b^a=bd,d^a=dg,f^a=fh,i^a=i^27,d^b=dh,e^b=eg,i^c=i^72,i^e=i^72556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1086902);