Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D4×C7⋊SL(2,𝔽3) |
| unambiguous semidirect product | C4⋊(C2×C7⋊SL(2,𝔽3)) |
| unambiguous semidirect product | (C7×D4)⋊SL(2,𝔽3) |
| unambiguous semidirect product | (D4×Q8)⋊ΓL(1,𝔽8) |
| Fitting, Hall | C7×D4×Q8 ⋊ C3 |
| Sylow | D4×Q8 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ D4×SL(2,𝔽3) |
210 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10070);