Finite Group DatabasebetaFinite Group Databasebeta| order | 6074 |
| automorphism | Aut(G) order 9220332 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3037 |
| unambiguous semidirect product | C3037⋊C2 |
| Fitting, socle, derived, Sylow | C3037 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3037 | C2 |
| LCS | G ▷ C3037 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3037|b^a=b^30361520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27131516, C2×D3037, D3037⋊C3, … |
| maximal normal subgroup of | #27131516, C2×D3037, D3037⋊C3, … |
| maximal quotient of | Dic3037, C2×D3037, C3×D3037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6074, 1);