Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C89×#1394 ⋊ C2 |
| Sylow | C89 ⋊ #12587 |
794 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 151 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=h,e^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,c^b=ch,e^b=egh,i^c=i^88,e^d=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 84554);