Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×M32×C89 ⋊ C2 |
| Sylow | C89 ⋊ #11593 |
450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=e,c^2=h,d^2=fh,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^88,c^b=ch,d^b=df,f^b=fh,i^b=i^883584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 79318);