Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | #127×C3⋊D21 |
| Fitting | C32×C7×#127 ⋊ C2 |
| Hall | C32×C7 ⋊ C2×#127 |
| Sylow | C32 ⋊ D7×#127 |
| Sylow | C7 ⋊ C3⋊D3×#127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C3⋊D21 |
| commutator, socle, cosocle | C22×C32×C7 | C24 |
| Fitting | C32×C7×#127 | C2 |
| hypercenter | #127 | C3⋊D21 |
| hypocenter | C32×C7 | C2×#127 |
| LCS | G ▷ C22×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C22 ◁ #127 | |
2988 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 2988 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) = 1008 |
462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C3⋊D3×#127, #127×C3⋊(C3⋊AGL(1,𝔽7)), #72247048 |
| maximal normal subgroup of | D7×C3⋊D3×#127, #127×C3⋊(C3⋊AGL(1,𝔽7)), #72247048 |
Past the SmallGroups library coverage — no SmallGroups id.