Finite Group DatabasebetaFinite Group Databasebeta| order | 12096 |
| isoclinism | isoclinic class of SU(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| direct product | C2×SU(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2 | SU(3,𝔽3) |
| commutator, hypocenter | SU(3,𝔽3) | C2 |
| Frattini | C1 | G |
| LCS | G ▷ SU(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
104 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
28 conjugacy classes — view the full character table.
| maximal subgroup of | C4×SU(3,𝔽3) |
| maximal normal subgroup of | C4×SU(3,𝔽3) |
| maximal quotient of | C4×SU(3,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.