Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M32×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#2110 |
738 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,e^2=g,g^2=h,b^a=bg,f^a=fh,c^b=ch,e^b=eh,i^b=i^27,i^d=i^72,i^f=i^72808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1113399);