Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#357×C89 ⋊ C2 |
| Sylow | C89 ⋊ #12731 |
1190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=f,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dg,g^b=gh,i^c=i^881994 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 85208);