Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C73×H(7,𝔽2) ⋊ C2 |
| Sylow | C73 ⋊ #60388 |
4874 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|f^2=h,b^a=bf,c^a=cg,f^a=fh,i^a=i^72,f^b=fh,g^b=gh,f^c=fh,e^d=eh2398 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1036249);