Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C173 ⋊ #1784 |
564 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=f,b^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^80,f^b=fg,h^c=h^172,h^f=h^172892 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20345);