Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of AΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C4×AΓL(1,𝔽8) |
| unambiguous semidirect product | AGL(1,𝔽8)⋊(C2×C3×C4) |
| unambiguous semidirect product | (C2×AGL(1,𝔽8))⋊(C3×C4) |
| unambiguous semidirect product | (C2×C4×AGL(1,𝔽8))⋊C3 |
| Fitting, Sylow | C24×C4 ⋊ ΓL(1,𝔽8) |
| derived | AGL(1,𝔽8) ⋊ C2×C3×C4 |
| Hall | C2×C4×AGL(1,𝔽8) ⋊ C3 |
159 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 56 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×AGL(3,𝔽2), C2×AGL(1,𝔽5)×AΓL(1,𝔽8), C4×D3×AΓL(1,𝔽8) |
| maximal quotient of | C2×AGL(1,𝔽5)×AΓL(1,𝔽8), C4×D3×AΓL(1,𝔽8) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11306);