Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#272 |
| Fitting, derived, Hall | C11×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ D11 |
| Sylow | C11 ⋊ #272 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊D33 |
| commutator, Fitting, cosocle, hypocenter | C11×H(3,𝔽3) | C2 |
| socle | C3×C11 | C3⋊D3 |
| LCS | G ▷ C11×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 99 |
Polycyclic presentation:
2,3^2,11,3|b^a=b^2,c^a=c^2,d^a=d^10,c^b=ce65 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#272, ((C3⋊D3)⋊C3)⋊D11, C2×C11⋊#272, … |
| maximal normal subgroup of | D11×#272, ((C3⋊D3)⋊C3)⋊D11, C2×C11⋊#272, … |
| maximal quotient of | C11⋊#1084, C2×C11⋊#272, C11⋊#4181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 19);