Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C173 ⋊ #1453 |
190 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 84 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=cg,h^a=h^93,c^b=cf,h^b=h^80,h^d=h^172,h^e=h^172916 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19729);