Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C73 ⋊ #20321 |
542 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18688 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=g,c^2=gh,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eg,f^a=fh,i^a=i^72,c^b=cgh,d^b=de,e^b=eg,f^c=fh,i^c=i^72,e^d=eg1621 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 166852);