Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ #9546 |
444 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=df,c^2=dg,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,i^a=i^27,c^b=ch,i^b=i^27,e^c=eg,i^c=i^72,i^f=i^72568 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1090933);