Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #4245 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×D3)⋊Dic7 |
| unambiguous semidirect product | (C2×D3)⋊(C3×Dic7) |
| Hall | C32×C7 ⋊ C22⋊C4 |
| Sylow | C32 ⋊ C22⋊Dic7 |
| Sylow | C7 ⋊ C3×(C2×D3)⋊C4 |
152 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #72246631, C3×D7×(C2×D3)⋊C4, #72246678, … |
| maximal normal subgroup of | #72246631, C3×D7×(C2×D3)⋊C4, #72246678, … |
| maximal quotient of | C3×#10620514 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 313);