Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C89×#1352 ⋊ C2 |
| Sylow | C89 ⋊ #12122 |
458 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|b^2=fh,c^2=h,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=gh,i^a=i^88,d^b=df,e^b=egh,d^c=dg,i^c=i^88,e^d=eh1043 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 81780);