Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C89×#2536 ⋊ C2 |
| Sylow | C89 ⋊ #9997 |
622 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 101 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|c^2=g,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fh,i^a=i^88,c^b=cf,d^b=dg,d^c=dh,e^c=eh1709 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 70305);