Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D173⋊#331 |
| Sylow | C173 ⋊ C2×#331 |
360 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 84 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=e,d^2=g,e^2=fg,b^a=bd,d^a=df,h^a=h^80,d^b=dg,e^b=efg,h^c=h^172,h^e=h^172640 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20004);