Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| unambiguous semidirect product | D73⋊#2986 |
| Sylow | C73 ⋊ C2×#2986 |
1794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=f,c^2=f,g^2=h,b^a=bf,d^a=df,i^a=i^27,c^b=cfh,d^b=dh,i^e=i^72,i^g=i^72604 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1115452);