Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of SU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×SU(3,𝔽2) |
| Fitting, Sylow | C3×H(3,𝔽3) ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C32 | PSU(3,𝔽2) |
| commutator, cosocle | #272 | C22×C3 |
| Frattini | C3 | C3×PSU(3,𝔽2) |
| Fitting | C3×H(3,𝔽3) | Q8 |
| prime radical | C3×#272 | C22 |
| hypocenter | H(3,𝔽3) | C3×Q8 |
| LCS | G ▷ #272 ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
63 conjugacy classes of subgroups.
| transitive degree | μt(G) = 81 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#6249⋊C2, #13049186, D3×SU(3,𝔽2), … |
| maximal normal subgroup of | C3×#6249⋊C2, #13049186, D3×SU(3,𝔽2), … |
| maximal quotient of | C3×#88592, C2×C3×SU(3,𝔽2), C9×SU(3,𝔽2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 550);