Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of 3−1+2⋊PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | 3−1+2⋊PSU(3,𝔽2) |
| unambiguous semidirect product | (C9⋊PSU(3,𝔽2))⋊C3 |
| Fitting, Sylow | C32×3−1+2 ⋊ Q8 |
124 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^2=d,g^3=h,b^a=bd,e^a=f,f^a=e^2,g^a=g^2h^2,h^a=h^2,e^b=ef^2,f^b=e^2f^2,g^c=gh^2,e^d=e^2,f^d=f^242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3549);