Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #9866 |
476 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18688 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=def,c^2=eg,d^2=g,f^2=h,b^a=bd,c^a=ce,i^a=i^46,d^b=dg,f^b=fg,i^b=i^27,i^f=i^72580 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1091684);