Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #322×C173 ⋊ C2 |
| Sylow | C173 ⋊ #1454 |
178 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 89 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=d,b^2=e,d^2=f,e^2=g,c^a=cfg,c^b=cf,h^b=h^172,h^c=h^1723496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 2811);