Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
| direct product | C32×C3⋊#272 |
| unambiguous semidirect product | C3⋊(C32×#272) |
| Fitting, Sylow | C33×H(3,𝔽3) ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C32 |
| Frattini | C3 | C32×C3⋊(C3⋊D3) |
| Fitting | C33×H(3,𝔽3) | C2 |
| socle | C34 | C3⋊D3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C33 | |
3782 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13091502, C3×#11758090, #72222306, … |
| maximal normal subgroup of | C3×#11758090, #72222306, C32×((C3⋊D3)⋊C3)⋊D3, … |
| maximal quotient of | C3×#13091647, #72221905, #72221921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1761);