Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | D3×ΓL(1,𝔽8)⋊Q8 |
| unambiguous semidirect product | (D3×ΓL(1,𝔽8))⋊Q8 |
| unambiguous semidirect product | (D3×Dic14)⋊C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×Q8 |
| Sylow | C7 ⋊ C3×D3×Q8 |
164 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1159⋊C3, D3×#1157⋊C3, D3×Q8×AGL(1,𝔽7), … |
| maximal normal subgroup of | D3×#1159⋊C3, D3×#1157⋊C3, D3×Q8×AGL(1,𝔽7), … |
| maximal quotient of | #72246905, #72246906 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 530);