Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C89×#1280 ⋊ C2 |
| Sylow | C89 ⋊ #7103 |
692 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 83 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|a^2=d,c^2=f,d^2=g,b^a=bc,c^a=ce,e^a=eh,c^b=cf,d^b=def,i^b=i^88,d^c=dh1982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56313);