Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| isoclinism | isoclinic class of C11⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C11⋊((C3⋊D3)⋊C3) |
| unambiguous semidirect product | (C3⋊D33)⋊C3 |
| Fitting, Hall | C11×H(3,𝔽3) ⋊ C2 |
| derived | C32×C11 ⋊ C2×C3 |
| Sylow | H(3,𝔽3) ⋊ D11 |
| Sylow | C11 ⋊ (C3⋊D3)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C11 | C2×C3 |
| Frattini | C3 | C3×D33 |
| Fitting | C11×H(3,𝔽3) | C2 |
| socle | C3×C11 | C3×D3 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 99 |
Polycyclic presentation:
2,3^3,11|c^a=c^2,d^a=d^2,e^a=e^10,c^b=cd65 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 14);