Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C42×D3×C7 |
| Fitting | C2×C3×C42×C7 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C42×C7 |
| Hall | C3×C7 ⋊ C22×C42 |
996 conjugacy classes of subgroups; only the 606 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 606 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×D3×AGL(1,𝔽29), C2×C4×D3×C7×AGL(1,𝔽5) |
| maximal quotient of | C2×C4×D3×AGL(1,𝔽29), C2×C4×D3×C7×AGL(1,𝔽5) |
| automorphism group of | C5×Dic3×C29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10476);