Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#352×C89 ⋊ C2 |
| Sylow | C89 ⋊ #13044 |
724 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 95 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=df,c^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,c^b=ch,e^b=egh,i^b=i^88,d^c=dg,f^c=fg,e^d=eh,f^e=fh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 86847);