Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C4 |
| direct product | #127×C3⋊AGL(1,𝔽7) |
| Fitting | C3×C7×#127 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×#127 |
| Sylow | C7 ⋊ C3×D3×#127 |
2100 conjugacy classes of subgroups; only the 314 normal subgroups are shown.
This group has 2100 conjugacy classes of subgroups — too many to draw. Only its 314 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#127×AGL(1,𝔽7), #127×C3⋊(C3⋊AGL(1,𝔽7)), #453×C3⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | D3×#127×AGL(1,𝔽7), #453×C3⋊AGL(1,𝔽7), #72254460 |
| maximal quotient of | #127×C3⋊(C3⋊AGL(1,𝔽7)) |
Past the SmallGroups library coverage — no SmallGroups id.