Finite Group DatabasebetaFinite Group Databasebeta| order | 1932 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | D3×D7×C23 |
| unambiguous semidirect product | (D3×C7)⋊(C2×C23) |
| unambiguous semidirect product | (C3×D7)⋊(C2×C23) |
| unambiguous semidirect product | D21⋊(C2×C23) |
| Fitting, socle, Hall | C3×C7×C23 ⋊ C22 |
| derived, Hall | C3×C7 ⋊ C22×C23 |
| Hall | C7×C23 ⋊ C2×D3 |
| Hall | C3×C23 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D3×C23 |
| Sylow | C3 ⋊ C2×D7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D7 |
| commutator, cosocle, hypocenter | C3×C7 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C23 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C23 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 483 |
345 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C23×D49, D3×C7×D7×C23, D3×C23×C7⋊D7, … |
| maximal normal subgroup of | D3×C7×D7×C23, D3×D7×C23⋊C11, D3×C11×D7×C23, … |
| maximal quotient of | D3×C23×D49, D3×C7×D7×C23, D3×C23×C7⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1932, 20);