Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | #120×C3⋊D21 |
| Fitting | C32×C7×#120 ⋊ C2 |
| Hall | C32×C7 ⋊ C2×#120 |
| Sylow | C32 ⋊ D7×#120 |
| Sylow | C7 ⋊ C3⋊D3×#120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C3⋊D21 |
| commutator, socle, cosocle | C22×C32×C7 | C24 |
| Fitting | C32×C7×#120 | C2 |
| hypercenter | #120 | C3⋊D21 |
| hypocenter | C32×C7 | C2×#120 |
| LCS | G ▷ C22×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C22 ◁ #120 | |
3972 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 3972 conjugacy classes of subgroups — too many to draw. Only its 391 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C3⋊D3×#120, #120×C3⋊(C3⋊AGL(1,𝔽7)) |
| maximal normal subgroup of | D7×C3⋊D3×#120, #120×C3⋊(C3⋊AGL(1,𝔽7)) |
Past the SmallGroups library coverage — no SmallGroups id.