Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C173 ⋊ #1747 |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=e,b^2=f,c^2=d,d^2=g,b^a=bd,f^a=fg,h^a=h^172,e^b=eg,h^b=h^172,h^c=h^1721936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 4266);