Finite Group DatabasebetaFinite Group Databasebeta| order | 6912 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24×C3 |
| direct product | S4×A4⋊S4 |
| Fitting, socle | C26 ⋊ D3×C3⋊D3 |
| derived | A43 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A43 | C22 |
| Fitting, socle | C26 | D3×C3⋊D3 |
| LCS | G ▷ A43 | |
| UCS | C1 | |
3517 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 3517 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
70 conjugacy classes — view the full character table.
| holomorph of | C22×A4 |
Past the SmallGroups library coverage — no SmallGroups id.