Finite Group DatabasebetaFinite Group Databasebeta| order | 6378 |
| automorphism | Aut(G) order 6773436 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3189 |
| unambiguous semidirect product | C3⋊D1063 |
| unambiguous semidirect product | C1063⋊D3 |
| Fitting, socle, derived, Hall | C3×C1063 ⋊ C2 |
| Sylow | C1063 ⋊ D3 |
| Sylow | C3 ⋊ D1063 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C1063 | C2 |
| LCS | G ▷ C3×C1063 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1063|b^a=b^2,c^a=c^10621596 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1063, C2×D3189, D9567, … |
| maximal normal subgroup of | D3×D1063, C2×D3189, C3⋊(D1063⋊C3), … |
| maximal quotient of | Dic3189, C2×D3189, D9567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6378, 5);