Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of C11⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×C11⋊S4 |
| unambiguous semidirect product | C11⋊(C3×S4) |
| unambiguous semidirect product | A4⋊(C3×D11) |
| Fitting, socle | C22×C3×C11 ⋊ D3 |
| derived | C11×A4 ⋊ C2×C3 |
| Sylow | C11 ⋊ C3×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊S4 |
| commutator, cosocle, hypocenter | C11×A4 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C11 | D3 |
| LCS | G ▷ C11×A4 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 132 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×S4, D3×C11⋊S4, D33⋊S4, … |
| maximal normal subgroup of | C3×D11×S4, D3×C11⋊S4, D33⋊S4, … |
| maximal quotient of | C3×C11⋊#226, C3×C11⋊GL(2,𝔽3), C3×C11⋊SL(2,ℤ/4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 118);