Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | S4×AGL(2,𝔽3) |
| Fitting, socle | C22×C32 ⋊ D3×GL(2,𝔽3) |
| derived | A4×PSU(3,𝔽2)⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×PSU(3,𝔽2)⋊C3 | C22 |
| Fitting, socle | C22×C32 | D3×GL(2,𝔽3) |
| LCS | G ▷ A4×PSU(3,𝔽2)⋊C3 | |
| UCS | C1 | |
1276 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
55 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.