Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C32 |
| direct product | C2×C11×H(3,𝔽3) |
| unambiguous semidirect product | (C2×C32)⋊(C3×C11) |
| unambiguous semidirect product | (C2×C32×C11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C11 | C32 |
| commutator, Frattini, cosocle | C3 | C2×C32×C11 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C11 ◁ G | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 198 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2)(3,4,5,6,7,8,9,10,11,12,13)(14,15,17)(16,19,21)(18,22,20);(15,18,19)(17,21,22)242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 21);