Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #7117 |
230 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 71 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,b^2=h,c^2=f,d^2=g,e^2=h,g^2=h,b^a=bc,c^a=ce,f^a=fh,i^a=i^88,c^b=cf,d^b=defh,e^b=eh,g^b=gh,d^c=dh1448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56348);