Finite Group DatabasebetaFinite Group Databasebeta| order | 6022 |
| automorphism | Aut(G) order 9063110 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3011 |
| unambiguous semidirect product | C3011⋊C2 |
| Fitting, socle, derived, Sylow | C3011 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3011 | C2 |
| LCS | G ▷ C3011 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3011|b^a=b^30101507 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3011, C3×D3011, D9033, … |
| maximal normal subgroup of | C2×D3011, C3×D3011, D3011⋊C5, … |
| maximal quotient of | Dic3011, C2×D3011, C3×D3011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6022, 1);