Finite Group DatabasebetaFinite Group Databasebeta| order | 1782 |
| isoclinism | isoclinic class of C11⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | C3×C11⋊((C3⋊D3)⋊C3) |
| unambiguous semidirect product | C11⋊(C3×(C3⋊D3)⋊C3) |
| unambiguous semidirect product | (C3⋊D33)⋊C32 |
| unambiguous semidirect product | (C3×C3⋊D33)⋊C3 |
| Fitting, Hall | C3×C11×H(3,𝔽3) ⋊ C2 |
| derived | C32×C11 ⋊ C2×C32 |
| Sylow | C3×H(3,𝔽3) ⋊ D11 |
| Sylow | C11 ⋊ C3×(C3⋊D3)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C32×C11 | C2×C32 |
| Frattini | C3 | C32×D33 |
| Fitting | C3×C11×H(3,𝔽3) | C2 |
| socle | C32×C11 | C3×D3 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C3 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1782, 75);