Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#6474⋊C3 |
| Fitting | C3×C7×D8 ⋊ C2×C3 |
| Hall | #6474 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ AGL(1,ℤ/8) |
| Sylow | C7 ⋊ C32×AGL(1,ℤ/8) |
408 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,ℤ/8)×AGL(1,𝔽7), #72245389, #72245450, … |
| maximal normal subgroup of | C3×AGL(1,ℤ/8)×AGL(1,𝔽7), D3×#6474⋊C3, #72245680 |
| maximal quotient of | #72245389, #72245450, C3×#72245547 |
Past the SmallGroups library coverage — no SmallGroups id.