Finite Group DatabasebetaFinite Group Databasebeta| order | 6122 |
| automorphism | Aut(G) order 9366660 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3061 |
| unambiguous semidirect product | C3061⋊C2 |
| Fitting, socle, derived, Sylow | C3061 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3061 | C2 |
| LCS | G ▷ C3061 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3061|b^a=b^30601532 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27133617, C2×D3061, D3061⋊C3, … |
| maximal normal subgroup of | #27133617, C2×D3061, D3061⋊C3, … |
| maximal quotient of | Dic3061, C2×D3061, C3×D3061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6122, 1);