Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | PSU(3,𝔽2)⋊C3 |
| commutator, hypocenter | SU(3,𝔽2) | C9 |
| Fitting | #737 | SL(2,𝔽3) |
| socle | C3 | PSU(3,𝔽2)⋊C9 |
| prime radical | #272 | C22⋊C9 |
| cosocle | #10620032 | C3 |
| LCS | G ▷ SU(3,𝔽2) | |
| UCS | C1 ◁ C9 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 243 |
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
3^2,2^3,3^3|a^3=b,b^3=h,c^2=e,d^2=e,c^a=d,d^a=cde,f^a=fg,d^c=de,f^c=fg,g^c=fg^2h,f^d=g^2,g^d=fh,f^e=f^2h^2,g^e=g^2h,g^f=gh72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2294);