Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| isoclinism | isoclinic class of AGL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×AGL(2,𝔽3) |
| Fitting, socle | C23×C32 ⋊ GL(2,𝔽3) |
| derived | PSU(3,𝔽2)⋊C3 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | AGL(2,𝔽3) |
| commutator, cosocle, hypocenter | PSU(3,𝔽2)⋊C3 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32 | GL(2,𝔽3) |
| LCS | G ▷ PSU(3,𝔽2)⋊C3 | |
| UCS | C1 ◁ C23 | |
3256 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 3256 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
88 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.