Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C3 | C3×PSU(3,𝔽2)⋊C3 |
| commutator, cosocle, hypocenter | SU(3,𝔽2) | C32 |
| Fitting | C3×H(3,𝔽3) | SL(2,𝔽3) |
| prime radical | C3×#272 | A4 |
| hypercenter | C32 | PSU(3,𝔽2)⋊C3 |
| LCS | G ▷ SU(3,𝔽2) | |
| UCS | C1 ◁ C3 ◁ C32 | |
83 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^2,2^3,3^3|a^3=h,c^2=e,d^2=e,b^a=bh,c^a=d,d^a=cde,f^a=fg^2h^2,d^c=de,f^c=f^2g^2h,g^c=f^2g,f^d=fg^2h^2,g^d=f^2g^2,f^e=f^2h,g^e=g^2h^2,g^f=gh40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3445);