Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | C3⋊D3×#6445 |
| Fitting | C32×C7×C22⋊C4 ⋊ C22 |
| Hall | C32×C7 ⋊ C2×#120 |
| Sylow | C32 ⋊ C2×#6445 |
| Sylow | C7 ⋊ C3⋊D3×#120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D7×C3⋊D3 |
| commutator, socle, cosocle | C22×C32×C7 | C24 |
| Fitting | C32×C7×C22⋊C4 | C22 |
| hypercenter | C22⋊C4 | D7×C3⋊D3 |
| hypocenter | C32×C7 | C2×#120 |
| LCS | G ▷ C22×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
3972 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C3⋊D3×#120, C3⋊D3×#6445⋊C3 |
| maximal normal subgroup of | D7×C3⋊D3×#120, C3⋊D3×#6445⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.