Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #32695 |
642 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 22784 |
Polycyclic presentation:
2^8,89|a^2=efh,b^2=eh,c^2=fh,d^2=efh,g^2=h,b^a=be,c^a=cf,d^a=defh,c^b=cg,d^b=de,g^b=gh,i^b=i^88,g^c=gh,i^c=i^881976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 316369);