Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C173 ⋊ C2 |
| Sylow | C173 ⋊ #1898 |
598 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 101 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,b^a=bd,c^a=ce,d^a=dg,h^a=h^172,d^b=dg,f^b=fg3472 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 4963);