Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C3×C7×(C2×D3)⋊C4 |
| unambiguous semidirect product | (C2×D3)⋊(C3×C4×C7) |
| Fitting | C2×C32×C4×C7 ⋊ C2 |
| Hall | C32×C7 ⋊ C22⋊C4 |
| Sylow | C32 ⋊ C7×C22⋊C4 |
152 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#63921, C3×D7×(C2×D3)⋊C4, #72246666, … |
| maximal normal subgroup of | C7×#63921, C3×D7×(C2×D3)⋊C4, #72246666, … |
| maximal quotient of | C3×C7×#805 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 436);