Finite Group DatabasebetaFinite Group Databasebeta| order | 2688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D7×#5244 |
| Fitting | C3×C7×H(5,𝔽2) ⋊ C22 |
| Hall | C3×C7 ⋊ C2×B(4,𝔽2) |
| Sylow | C7 ⋊ C2×#5244 |
| Sylow | C3 ⋊ D7×B(4,𝔽2) |
2036 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 2036 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D7×B(4,𝔽2), AGL(1,𝔽7)×#5244 |
| maximal normal subgroup of | D3×D7×B(4,𝔽2), AGL(1,𝔽7)×#5244 |
Past the SmallGroups library coverage — no SmallGroups id.