Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | D4×M16×C73 ⋊ C2 |
| Sylow | C73 ⋊ #8991 |
578 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=dfg,d^2=g,e^2=h,f^2=h,b^a=bd,c^a=ce,i^a=i^72,d^b=dg,e^b=eh,f^b=fg,d^c=dh,e^c=eh,f^c=fh1852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 64427);