Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C173 ⋊ Q8×C16 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22144 |
Polycyclic presentation:
2^7,173|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,h^a=h^93,h^c=h^80,h^e=h^172940 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20924);