Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #13127 |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=df,c^2=d,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^88,c^b=cg,d^b=dh,f^b=fh,i^b=i^88,f^c=fh1982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 87346);