Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6229⋊C9 |
| Sylow | H(3,𝔽3)⋊C9 ⋊ Q8 |
201 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^2=d,c^3=e,b^a=bd,f^a=f^2,g^a=g^2h,f^c=fg,g^f=gh183 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 354);