Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×D4×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C32×D4) |
| unambiguous semidirect product | (D4×D7)⋊C32 |
| unambiguous semidirect product | (C3×D4×D7)⋊C3 |
| Fitting | C3×C7×D4 ⋊ C2×C3 |
| Hall | D4×D7 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D4 |
| Sylow | C7 ⋊ C2×C32×D4 |
324 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 641);