Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C89×#1342 ⋊ C2 |
| Sylow | C89 ⋊ #12299 |
324 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=fg,b^2=h,d^2=f,f^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fh,g^a=gh,i^a=i^88,d^b=dfh,e^b=egh,f^b=fh,d^c=dg,i^c=i^88,e^d=eh905 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 82899);