Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D3×AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×PSU(3,𝔽2)⋊C4 |
| unambiguous semidirect product | (D3×PSU(3,𝔽2))⋊C4 |
| Sylow | C33 ⋊ C2×#103 |
394 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×(PSU(3,𝔽2)⋊C3)⋊C4, #72260065 |
| maximal quotient of | #72260065 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46196);