Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3⋊D3×D28 |
| Fitting | C2×C32×C4×C7 ⋊ C22 |
| Hall | C32×C7 ⋊ C22×D4 |
| Sylow | C32 ⋊ C22×D28 |
| Sylow | C7 ⋊ C2×D4×C3⋊D3 |
1416 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 240 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×D7×C3⋊D3, C2×C3⋊D3×C4⋊AGL(1,𝔽7), #72245859, … |
| maximal normal subgroup of | C2×D4×D7×C3⋊D3, C2×C3⋊D3×C4⋊AGL(1,𝔽7), #72245859, … |
| maximal quotient of | C3⋊D3×#6437, C3⋊D3×#6445 |
Past the SmallGroups library coverage — no SmallGroups id.