Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of PSU(3,𝔽2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | PSU(3,𝔽2)⋊C27 |
| derived | PSU(3,𝔽2) ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | PSU(3,𝔽2)⋊C3 |
| commutator, hypocenter | PSU(3,𝔽2) | C27 |
| Fitting | C32×C9 | SL(2,𝔽3) |
| socle | C33 | Q8⋊C9 |
| prime radical | C3×C3⋊D3 | C22⋊C9 |
| cosocle | C9×PSU(3,𝔽2) | C3 |
| LCS | G ▷ PSU(3,𝔽2) | |
| UCS | C1 ◁ C9 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
3^3,2^3,3^2|a^3=b,b^3=c,d^2=f,e^2=f,d^a=e,e^a=def,g^a=gh,e^d=ef,g^d=gh,h^d=gh^2,g^e=h^2,h^e=g,g^f=g^2,h^f=h^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2291);