Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C173 ⋊ #2032 |
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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=d,b^2=d,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,f^b=fg,h^b=h^172,d^c=dg1915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 5687);