Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #12680 |
958 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=f,f^2=g,g^2=h,b^a=bd,c^a=ce,c^b=ch,i^c=i^883608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 85003);