Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #10361 |
392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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=dg,b^2=d,c^2=g,e^2=g,f^2=gh,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^88,c^b=cf,e^b=eh,f^b=fgh,e^c=eg,f^c=fgh,i^c=i^881706 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 72652);