Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #13063443⋊C16 |
| Sylow | C173 ⋊ #1312 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22144 |
Polycyclic presentation:
2^7,173|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^80,h^c=h^1721456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19424);