Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #9229 |
646 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=dfgh,d^2=gh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^88,c^b=cg,d^b=dh,e^b=eh,f^b=fh,i^b=i^88,d^c=dh,e^c=eh,f^c=fh1718 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 65807);