Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C73×#2080 ⋊ C2 |
| Sylow | C73 ⋊ #23833 |
616 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=e,d^2=ef,f^2=h,g^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,i^b=i^72,e^c=eh,f^c=fh,g^c=gh,i^d=i^72988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 200449);