Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C4×D3×AGL(1,𝔽8) |
| unambiguous semidirect product | (C23×C4×D3)⋊C7 |
| Fitting | C23×C3×C4 ⋊ C2×C7 |
| derived | C23×C3 ⋊ C2×C4×C7 |
| Hall | C23×C4×D3 ⋊ C7 |
| Sylow | C3 ⋊ C2×C4×AGL(1,𝔽8) |
254 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×AΓL(1,𝔽8) |
| maximal normal subgroup of | C4×D3×AΓL(1,𝔽8) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11312);