Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C89×#2274 ⋊ C2 |
| Sylow | C89 ⋊ #9476 |
818 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 111 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=g,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^88,e^b=eh,d^c=dh,f^c=fh3041 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 67372);