Finite Group DatabasebetaFinite Group Databasebeta| order | 15552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D32×AGL(2,𝔽3) |
| Fitting, socle | C34 ⋊ C22×GL(2,𝔽3) |
| derived | C32×PSU(3,𝔽2)⋊C3 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×PSU(3,𝔽2)⋊C3 | C23 |
| Fitting, socle | C34 | C22×GL(2,𝔽3) |
| LCS | G ▷ C32×PSU(3,𝔽2)⋊C3 | |
| UCS | C1 | |
3216 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 3216 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
99 conjugacy classes — view the full character table.
| holomorph of | C32×D3 |
Past the SmallGroups library coverage — no SmallGroups id.