Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #12902 |
278 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=d,c^2=e,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^27,c^b=cg,e^b=eh,i^b=i^72,d^c=dh,i^c=i^72,i^f=i^72448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1096909);