Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C89×#1747 ⋊ C2 |
| Sylow | C89 ⋊ #22286 |
820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=g,b^2=egh,c^2=ef,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^88,c^b=ce,f^b=fh,g^c=gh1982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 183499);