Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | D3×S42 |
| Fitting, socle | C24×C3 ⋊ C2×D32 |
| derived | C3×A42 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×A42 | C23 |
| Fitting, socle | C24×C3 | C2×D32 |
| LCS | G ▷ C3×A42 | |
| UCS | C1 | |
2892 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 2892 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
75 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.