Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #121×C73 ⋊ C8 |
| Sylow | C73 ⋊ #8939 |
768 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=dfg,d^2=g,f^2=h,b^a=bd,c^a=ce,i^a=i^63,d^b=dg,f^b=fg,i^b=i^10,i^f=i^27,i^h=i^72202 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116948);