Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C23×C4×C173 ⋊ C4 |
| Sylow | C173 ⋊ #1799 |
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=f,b^2=d,b^a=bd,c^a=ce,e^a=eg,h^a=h^80,f^c=fg,h^f=h^1721408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20370);