Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of PSU(3,𝔽2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
| direct product | C3×PSU(3,𝔽2)⋊C3 |
| unambiguous semidirect product | PSU(3,𝔽2)⋊C32 |
| unambiguous semidirect product | (C3×PSU(3,𝔽2))⋊C3 |
| Fitting, socle | C33 ⋊ SL(2,𝔽3) |
| derived | PSU(3,𝔽2) ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | PSU(3,𝔽2)⋊C3 |
| commutator, cosocle, hypocenter | PSU(3,𝔽2) | C32 |
| Frattini | C1 | G |
| Fitting, socle | C33 | SL(2,𝔽3) |
| LCS | G ▷ PSU(3,𝔽2) | |
| UCS | C1 ◁ C3 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24 |
30 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 702);