Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | D7×C22⋊C4×C3⋊D3 |
| Fitting | C32×C7×C22⋊C4 ⋊ C22 |
| Hall | C32×C7 ⋊ C22×C22⋊C4 |
| Sylow | C32 ⋊ C2×D7×C22⋊C4 |
| Sylow | C7 ⋊ C2×C22⋊C4×C3⋊D3 |
4044 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C3⋊D3×#120, C22⋊C4×C3⋊D3×AGL(1,𝔽7) |
| maximal normal subgroup of | D7×C3⋊D3×#120, C22⋊C4×C3⋊D3×AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.