Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C8×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×C4×C8) |
| unambiguous semidirect product | (C4×C8×D7)⋊C3 |
| Fitting | C4×C7×C8 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C2×C3×C4×C8 |
| Hall | C4×C8×D7 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C4×C8 |
324 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 873);