Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C89×#2433 ⋊ C2 |
| Sylow | C89 ⋊ #9946 |
1060 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 109 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|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fgh,i^a=i^88,c^b=cf,d^b=dg,e^b=eg,d^c=dh,e^c=eg1709 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 69988);