Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M32×C173 ⋊ C2 |
| Sylow | C173 ⋊ #2169 |
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,c^b=cg,h^b=h^1723496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 6340);