Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #7265 |
314 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 314 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=d,b^2=e,c^2=f,d^2=h,e^2=h,f^2=h,g^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fh,g^a=gh,c^b=cg,d^b=dh,f^b=fh,g^b=gh,i^b=i^881982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56732);