Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #137×C173 ⋊ C4 |
| Sylow | C173 ⋊ #1906 |
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2768 |
Polycyclic presentation:
2^7,173|a^2=f,b^2=df,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^93,d^b=dg,e^b=eg,f^b=fg,h^b=h^80,d^c=dg,e^c=eg,f^c=fg,h^f=h^172505 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20548);