Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C89 ⋊ #32701 |
628 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=fg,c^2=ef,d^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,f^a=fh,g^a=gh,i^a=i^88,c^b=cg,d^b=de,f^b=fh,g^c=gh,i^c=i^881178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 316448);