Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | C7×C3⋊D3×#127 |
| Fitting | C32×C7×#127 ⋊ C2 |
| Hall | C32×C7 ⋊ C2×#127 |
| Sylow | C32 ⋊ C2×C7×#127 |
2988 conjugacy classes of subgroups; only the 470 normal subgroups are shown.
This group has 2988 conjugacy classes of subgroups — too many to draw. Only its 470 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1008 |
588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C3⋊D3×#127, C3⋊D3×ΓL(1,𝔽8)×#127, C7×#11864777, … |
| maximal normal subgroup of | D7×C3⋊D3×#127, C3⋊D3×ΓL(1,𝔽8)×#127, C7×#11864777, … |
Past the SmallGroups library coverage — no SmallGroups id.