Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | D3×A4⋊AGL(1,𝔽7) |
| Fitting, socle | C22×C3×C7 ⋊ C2×C3×D3 |
| derived | C3×C7×A4 ⋊ C22×C3 |
| Sylow | C7 ⋊ C3×D3×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C7×A4 | C22×C3 |
| Fitting, socle | C22×C3×C7 | C2×C3×D3 |
| LCS | G ▷ C3×C7×A4 | |
| UCS | C1 | |
326 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×S4×AGL(1,𝔽7), S4×A4⋊AGL(1,𝔽7) |
| maximal normal subgroup of | D3×S4×AGL(1,𝔽7) |
| maximal quotient of | S4×A4⋊AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.