Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of A4×D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×D33 |
| unambiguous semidirect product | C3⋊(A4×D11) |
| unambiguous semidirect product | C11⋊(D3×A4) |
| unambiguous semidirect product | (C22×D33)⋊C3 |
| Fitting, socle, derived | C22×C3×C11 ⋊ C2×C3 |
| Sylow | C11 ⋊ D3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C3×C11 | C2×C3 |
| LCS | G ▷ C22×C3×C11 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 132 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D33, D33⋊S4, D3×A4×D11, … |
| maximal normal subgroup of | S4×D33, D33⋊S4, D3×A4×D11, … |
| maximal quotient of | C3⋊(C11⋊(#41⋊C3)), SL(2,𝔽3)×D33, A4×Dic33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 123);