Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C89×#1400 ⋊ C2 |
| Sylow | C89 ⋊ #7424 |
146 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 41 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|a^2=d,c^2=fgh,d^2=h,e^2=g,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fgh,g^a=gh,i^a=i^88,c^b=cf,d^b=defgh,e^b=egh,f^b=fgh,g^b=gh,i^b=i^88,d^c=dh1967 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 57142);