Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #8771 |
426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=gh,c^2=dh,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^b=fg,e^c=eh,f^c=fg,i^c=i^881451 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 63166);