Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C8×C16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #7068 |
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=h,b^a=bc,c^a=ce,e^a=eg,i^a=i^88,c^b=ce,e^b=eg,i^b=i^885720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56218);