Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D173⋊#413 |
| Sylow | C173 ⋊ C2×#413 |
756 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2768 |
Polycyclic presentation:
2^7,173|a^2=f,c^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^80,f^b=fg,h^d=h^172,h^f=h^172904 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 21118);