Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C89 ⋊ #9165 |
486 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=dfg,d^2=gh,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=i^88,d^b=dh,e^b=eg,f^b=fh,d^c=dg,e^c=eg,f^c=fg2243 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 65405);