Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #12415 |
272 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 22784 |
Polycyclic presentation:
2^8,89|a^2=gh,b^2=g,c^2=gh,d^2=fh,e^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=egh,f^a=fh,i^a=i^88,d^b=df,e^b=eg,f^b=fh,i^b=i^88,d^c=dg,e^c=egh1703 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 83679);