Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C34 |
| direct product | C3×D9×H(3,𝔽3) |
| Fitting, Sylow | C3×C9×H(3,𝔽3) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C32×D9 |
| commutator, cosocle | C3×C9 | C2×C33 |
| Frattini | C32 | C33×D3 |
| Fitting | C3×C9×H(3,𝔽3) | C2 |
| socle | C33 | C32×D3 |
| hypercenter | C3×H(3,𝔽3) | D9 |
| hypocenter | C9 | C2×C3×H(3,𝔽3) |
| LCS | G ▷ C3×C9 ▷ C9 | |
| UCS | C1 ◁ C32 ◁ C3×H(3,𝔽3) | |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C3×H(3,𝔽3)×AGL(1,ℤ/9), #72243834, D9×C9⋊H(3,𝔽3), … |
| maximal normal subgroup of | C3×H(3,𝔽3)×AGL(1,ℤ/9), #72243834, D9×C9⋊H(3,𝔽3), … |
| maximal quotient of | D9×C9⋊H(3,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1432);