Finite Group DatabasebetaFinite Group Databasebeta| order | 2142 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D51 |
| unambiguous semidirect product | C3⋊(C3×C7×D17) |
| unambiguous semidirect product | C17⋊(C3×D3×C7) |
| Fitting, socle, Hall | C32×C7×C17 ⋊ C2 |
| derived | C3×C17 ⋊ C2×C3×C7 |
| Hall | C32×C17 ⋊ C2×C7 |
| Hall | C7×C17 ⋊ C3×D3 |
| Hall | C32×C7 ⋊ D17 |
| Sylow | C17 ⋊ C3×D3×C7 |
| Sylow | C32 ⋊ C7×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C17 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C3×C7 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 714 |
567 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C7×D17, C3×D7×D51, C3×D21⋊D17, … |
| maximal normal subgroup of | C3×D3×C7×D17, C3×D7×D51, C3×D21⋊D17, … |
| maximal quotient of | C3×C7×Dic51, C2×C3×C7×D51, C3×C49×D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2142, 26);