Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D173⋊#423 |
| Sylow | C173 ⋊ C2×#423 |
576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=f,b^2=e,f^2=g,b^a=be,c^a=cg,h^a=h^80,h^d=h^172,h^f=h^1721432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 21146);