Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×#135×C73 ⋊ C2 |
| Sylow | C73 ⋊ #60167 |
2706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=g,c^2=g,e^2=h,f^2=h,b^a=bf,d^a=dh,f^a=fh,f^b=fh,d^c=dh,i^d=i^722104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1033735);