Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C173 ⋊ #1997 |
260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=def,c^2=e,f^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,h^b=h^1722440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 5498);