Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#14583829 |
| Sylow | C173 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22144 |
Polycyclic presentation:
2^7,173|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^80,c^b=ce,h^d=h^172916 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19476);