Finite Group DatabasebetaFinite Group Databasebeta| order | 6054 |
| automorphism | Aut(G) order 6102432 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3027 |
| unambiguous semidirect product | C3⋊D1009 |
| unambiguous semidirect product | C1009⋊D3 |
| Fitting, socle, derived, Hall | C3×C1009 ⋊ C2 |
| Sylow | C1009 ⋊ D3 |
| Sylow | C3 ⋊ D1009 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C1009 | C2 |
| LCS | G ▷ C3×C1009 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1009|b^a=b^2,c^a=c^10081515 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1009, C2×D3027, D9081, … |
| maximal normal subgroup of | D3×D1009, C2×D3027, C3⋊(D1009⋊C3), … |
| maximal quotient of | Dic3027, C2×D3027, D9081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6054, 5);