Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of D9⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C34 |
| direct product | C3×D9⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×D9)⋊H(3,𝔽3) |
| Fitting, Sylow | C3×C9⋊H(3,𝔽3) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×AGL(1,ℤ/9) |
| commutator, cosocle | C3×C9 | C2×C33 |
| Frattini | C32 | C33×D3 |
| Fitting | C3×C9⋊H(3,𝔽3) | C2 |
| socle | C33 | C32×D3 |
| hypercenter | C33 | AGL(1,ℤ/9) |
| hypocenter | C9 | C2×C3×H(3,𝔽3) |
| LCS | G ▷ C3×C9 ▷ C9 | |
| UCS | C1 ◁ C32 ◁ C33 | |
584 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D9⋊H(3,𝔽3), C3×H(3,𝔽3)×AGL(1,ℤ/9), #72243817, … |
| maximal normal subgroup of | C9×D9⋊H(3,𝔽3), C3×H(3,𝔽3)×AGL(1,ℤ/9), #72243817, … |
| maximal quotient of | C9×D9⋊H(3,𝔽3), #72243827, #72243844 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1483);