Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×C3⋊AGL(1,𝔽7) |
| Fitting | C3×C7×M16 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×M16 |
| Sylow | C7 ⋊ C3×D3×M16 |
292 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 96 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 | #100×C3⋊AGL(1,𝔽7), D3×M16×AGL(1,𝔽7), #72244576, … |
| maximal normal subgroup of | #100×C3⋊AGL(1,𝔽7), D3×M16×AGL(1,𝔽7), #72244576, … |
| maximal quotient of | #72254160 |
Past the SmallGroups library coverage — no SmallGroups id.