Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C89 ⋊ #11383 |
926 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 251 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=g,b^2=f,c^2=fh,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^88,c^b=cf,g^b=gh2516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 78484);