Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D32×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D32×D11 |
| unambiguous semidirect product | (C3×D3×D11)⋊C2 |
| unambiguous semidirect product | (C3⋊D3×D11)⋊C2 |
| unambiguous semidirect product | (D3×D33)⋊C2 |
| Fitting, socle, derived, Hall | C32×C11 ⋊ C23 |
| Sylow | C11 ⋊ C2×D32 |
| Sylow | C32 ⋊ C22×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C11 | C23 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 66 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | D11×GO+(4,𝔽2), C2×D32×D11, D32×AGL(1,𝔽11), … |
| maximal normal subgroup of | D11×GO+(4,𝔽2), C2×D32×D11, D32×AGL(1,𝔽11), … |
| maximal quotient of | D3×Dic3×D11, D11×#624, D32×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 116);