Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C89×#1536 ⋊ C2 |
| Sylow | C89 ⋊ #8475 |
932 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 111 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=f,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^88,d^b=dh,e^b=eh,f^b=fgh,d^c=dh,f^c=fg,i^c=i^881184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 61820);