Finite Group DatabasebetaFinite Group Databasebeta| order | 6006 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×D39 |
| unambiguous semidirect product | C3⋊(C7×C11×D13) |
| unambiguous semidirect product | C13⋊(D3×C7×C11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | D39 |
| commutator, hypocenter | C3×C13 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C13 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C7×C11 | |
32 conjugacy classes of subgroups.
1617 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×C11×D13, C7×D11×D39, C7×D33⋊D13, … |
| maximal normal subgroup of | D3×C7×C11×D13, C7×D11×D39, C7×D33⋊D13, … |
| maximal quotient of | C7×C11×Dic39, C2×C7×C11×D39, C7×C11×D117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6006, 14);