Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×#101×C89 ⋊ C2 |
| Sylow | C89 ⋊ #11015 |
1242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=g,b^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,f^b=fh,g^b=gh,f^c=fh,i^c=i^881982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 76315);