Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C73×#1809 ⋊ C2 |
| Sylow | C73 ⋊ #25357 |
832 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=efh,b^2=f,c^2=h,d^2=eh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^72,c^b=cg,d^b=dh,i^b=i^72,f^c=fh,g^c=gh,i^c=i^72,i^d=i^721198 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 219939);