Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C173 ⋊ #1330 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=d,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^80,c^b=ceg,d^b=dg,h^b=h^172,h^d=h^172898 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19463);