Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×D3×D11 |
| unambiguous semidirect product | (D3×C11)⋊(C22×C3) |
| unambiguous semidirect product | (C3×D11)⋊(C22×C3) |
| unambiguous semidirect product | D33⋊(C22×C3) |
| Fitting, socle | C2×C32×C11 ⋊ C22 |
| derived | C3×C11 ⋊ C23×C3 |
| Hall | C32×C11 ⋊ C23 |
| Sylow | C11 ⋊ C22×C3×D3 |
| Sylow | C32 ⋊ C22×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×D11 |
| commutator, cosocle, hypocenter | C3×C11 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C11 | C22 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2×C3 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic3×D11, D11×#625, D11×#626, … |
| maximal normal subgroup of | D3×Dic3×D11, D11×#625, D11×#626, … |
| maximal quotient of | C3×D11×Dic6, C3×#10587227, C3×#10587228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 126);