Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×#419×C89 ⋊ C2 |
| Sylow | C89 ⋊ #21006 |
1654 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=g,b^2=egh,d^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^88,d^b=dh,e^b=eh,f^b=fh,g^b=gh,i^b=i^88,e^c=eh,f^c=fh,g^c=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, 171536);