Finite Group DatabasebetaFinite Group Databasebeta| order | 1332 |
| isoclinism | isoclinic class of D3×D111 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D111 |
| unambiguous semidirect product | (C3×D3)⋊D37 |
| unambiguous semidirect product | (D3×C37)⋊D3 |
| Fitting, socle, derived, Hall | C32×C37 ⋊ C22 |
| Sylow | C37 ⋊ D32 |
| Sylow | C32 ⋊ C2×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C37 | C22 |
| LCS | G ▷ C32×C37 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 222 |
171 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C11×D111, D3×D1221, D33×D111, … |
| maximal normal subgroup of | D3×C11×D111, D3×C13×D111, D3×C17×D111, … |
| maximal quotient of | D3×C11×D111, D3×D1221, D33×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1332, 51);