Finite Group DatabasebetaFinite Group Databasebeta| order | 24192 |
| isoclinism | isoclinic class of SU(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| general unitary | GU(3,𝔽3) |
| direct product | C4×SU(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4 | SU(3,𝔽3) |
| commutator, hypocenter | SU(3,𝔽3) | C4 |
| Frattini, cosocle | C2 | C2×SU(3,𝔽3) |
| socle, prime radical | C2×SU(3,𝔽3) | C2 |
| LCS | G ▷ SU(3,𝔽3) | |
| UCS | C1 ◁ C4 | |
199 conjugacy classes of subgroups; only the 6 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 6 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
56 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.