Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D3×ΓL(1,𝔽8)⋊C4 |
| unambiguous semidirect product | (D3×ΓL(1,𝔽8))⋊(C3×C4) |
| unambiguous semidirect product | (D3×Dic7)⋊C32 |
| unambiguous semidirect product | (C3×D3×Dic7)⋊C3 |
| derived | C3×C7 ⋊ C2×C32×C4 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×C4 |
| Sylow | C7 ⋊ C32×C4×D3 |
240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 602);