Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×(C3⋊AGL(1,𝔽7))⋊C4 |
| derived | C3×C7 ⋊ C2×C3×C42 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×C42 |
| Sylow | C7 ⋊ C3×C42×D3 |
462 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 161 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 | #72244257, C42×D3×AGL(1,𝔽7), C4×#13094713, … |
| maximal normal subgroup of | #72244257, C42×D3×AGL(1,𝔽7), #72254340, … |
| maximal quotient of | C4×#13094713 |
Past the SmallGroups library coverage — no SmallGroups id.