Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C73×#1389 ⋊ C2 |
| Sylow | C73 ⋊ #12841 |
358 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=dg,d^2=gh,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^b=i^72,e^c=eh,f^c=fh,i^c=i^721204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 85764);