Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | D3×C7×H(5,𝔽2) |
| Fitting | C3×C7×H(5,𝔽2) ⋊ C2 |
| Hall | C3×C7 ⋊ C2×H(5,𝔽2) |
| Sylow | C3 ⋊ C2×C7×H(5,𝔽2) |
1796 conjugacy classes of subgroups; only the 890 normal subgroups are shown.
This group has 1796 conjugacy classes of subgroups — too many to draw. Only its 890 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
357 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D7×H(5,𝔽2), D3×C7×B(4,𝔽2), D3×#90016, … |
| maximal normal subgroup of | D3×D7×H(5,𝔽2), D3×C7×B(4,𝔽2), D3×#90016, … |
| maximal quotient of | C7×#10596675 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11651);