Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C73×#1378 ⋊ C2 |
| Sylow | C73 ⋊ #12851 |
416 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^b=fh,i^b=i^72,e^c=eh1642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 85802);