Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×M16×C73 ⋊ C4 |
| Sylow | C73 ⋊ #12589 |
752 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,d^2=h,f^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,i^a=i^27,c^b=ch,e^b=egh,e^d=eh,i^e=i^72766 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1095889);