Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×#66681⋊C3 |
| Fitting | C2×C3×C4×C7 ⋊ C22×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C22×D4 |
| Sylow | C7 ⋊ C2×C3×D3×D4 |
998 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×D4×AGL(1,𝔽7), #72244221, #72244257, … |
| maximal normal subgroup of | C2×D3×D4×AGL(1,𝔽7), #72244221, #72244257, … |
| maximal quotient of | #72244221, #72244271, #72245617, … |
Past the SmallGroups library coverage — no SmallGroups id.