Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
| direct product | H(3,𝔽3)×C3⋊D9 |
| unambiguous semidirect product | C3⋊(D9×H(3,𝔽3)) |
| Fitting, Sylow | C3×C9×H(3,𝔽3) ⋊ C2 |
587 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 587 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | #72243650, H(3,𝔽3)×C3⋊AGL(1,ℤ/9), (C3⋊D3)⋊C3×C3⋊D9, … |
| maximal normal subgroup of | H(3,𝔽3)×C3⋊AGL(1,ℤ/9), (C3⋊D3)⋊C3×C3⋊D9, D3×D9×H(3,𝔽3), … |
| maximal quotient of | #72243650 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1433);