Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #8054 |
564 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 167 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=e,b^2=f,c^2=h,d^2=g,e^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fgh,d^b=dh,i^c=i^881748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 59709);