Finite Group DatabasebetaFinite Group Databasebeta| order | 2046 |
| isoclinism | isoclinic class of D341 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D341 |
| unambiguous semidirect product | C11⋊(C3×D31) |
| Fitting, socle, Hall | C3×C11×C31 ⋊ C2 |
| derived, Hall | C11×C31 ⋊ C2×C3 |
| Hall | C3×C31 ⋊ D11 |
| Hall | C3×C11 ⋊ D31 |
| Sylow | C31 ⋊ C3×D11 |
| Sylow | C11 ⋊ C3×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D341 |
| commutator, cosocle, hypocenter | C11×C31 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C31 | C2 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1023 |
516 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D31, D3×D341, D33⋊D31, … |
| maximal normal subgroup of | C3×D11×D31, D3×D341, D33⋊D31, … |
| maximal quotient of | C3×Dic341, C2×C3×D341, C3×C7×D341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2046, 5);