Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C89×#1423 ⋊ C2 |
| Sylow | C89 ⋊ #7537 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=d,c^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,c^b=ce,e^b=ef,f^b=fg,g^b=gh,i^b=i^881742 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 57445);