Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C3×D7×#120 |
| Fitting | C3×C7×#120 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×#120 |
| Sylow | C7 ⋊ C2×C3×#120 |
1324 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 262 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D7×#120, C3×#120×AGL(1,𝔽7), C3×D7×B(4,𝔽2), … |
| maximal normal subgroup of | D3×D7×#120, C3×#120×AGL(1,𝔽7), C3×D7×B(4,𝔽2), … |
| maximal quotient of | C3×D7×B(4,𝔽2), C3×D7×#453, #72245959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10220);