Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C173 ⋊ #2110 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,h^a=h^172,c^b=cg,d^b=dg3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 6115);