Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×D7×C3⋊C8 |
| derived | C3×C7 ⋊ C2×C3×C8 |
| Hall | C32×C7 ⋊ C2×C8 |
| Sylow | C32 ⋊ C8×D7 |
| Sylow | C7 ⋊ C2×C3×C3⋊C8 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3710, C3×D7×#208, D7×#3712, … |
| maximal normal subgroup of | D7×#3710, C3×D7×#208, D7×#3712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 293);