Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×#127×C89 ⋊ C2 |
| Sylow | C89 ⋊ #23906 |
2502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1424 |
Polycyclic presentation:
2^8,89|f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=cg,f^b=fh,e^c=eh,f^c=fh,i^c=i^88,f^d=fh2510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 201199);