Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#272 |
| Fitting, Hall | C11×H(3,𝔽3) ⋊ C2 |
| derived, Sylow | H(3,𝔽3) ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3×C11 | C3⋊D3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C11 |
| Frattini | C3 | C11×C3⋊D3 |
| Fitting | C11×H(3,𝔽3) | C2 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C3×C11 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 99 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#1088, C11⋊#1088, D11×#272, … |
| maximal normal subgroup of | C11×#1088, C11⋊#1088, D11×#272, … |
| maximal quotient of | C11×#1084, C2×C11×#272, C11×#4181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 17);