Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×#344×C73 ⋊ C2 |
| Sylow | C73 ⋊ #10941 |
904 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=ef,f^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^72,d^b=dh,e^b=eh,f^b=fh,i^b=i^72,d^c=dh1642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 75916);