Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×(C3⋊AGL(1,ℤ/9))⋊C4 |
| unambiguous semidirect product | (C2×(C3⋊D9)⋊C4)⋊C3 |
| derived | C3×C9 ⋊ C22×C3×C4 |
| Sylow | C3×3−1+2 ⋊ C22×C4 |
438 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14516827, C2×#88668⋊C3, #72219964, … |
| maximal normal subgroup of | C2×#88668⋊C3, #72219964, #72220001, … |
| maximal quotient of | C2×#14516827, #72219893, #72220050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2338);