Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of A4×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×D11 |
| unambiguous semidirect product | C11⋊(C2×C3×A4) |
| unambiguous semidirect product | (C22×D11)⋊C32 |
| unambiguous semidirect product | (C22×C3×D11)⋊C3 |
| Fitting, socle | C22×C3×C11 ⋊ C2×C3 |
| derived | C22×C11 ⋊ C2×C32 |
| Hall | C22×D11 ⋊ C32 |
| Sylow | C11 ⋊ C2×C3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×D11 |
| commutator, cosocle, hypocenter | C22×C11 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C11 | C2×C3 |
| LCS | G ▷ C22×C11 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×S4, D11×C3⋊S4, D3×A4×D11, … |
| maximal normal subgroup of | C3×D11×S4, D11×C3⋊S4, D3×A4×D11, … |
| maximal quotient of | C3×C11⋊(#41⋊C3), C3×D11×SL(2,𝔽3), C3×A4×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 121);