Finite Group DatabasebetaFinite Group Databasebeta| order | 8634 |
| automorphism | Aut(G) order 12415692 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4317 |
| unambiguous semidirect product | C3⋊D1439 |
| unambiguous semidirect product | C1439⋊D3 |
| Fitting, socle, derived, Hall | C3×C1439 ⋊ C2 |
| Sylow | C1439 ⋊ D3 |
| Sylow | C3 ⋊ D1439 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C1439 | C2 |
| LCS | G ▷ C3×C1439 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1439|b^a=b^2,c^a=c^14382160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1439, C2×D4317, D12951, … |
| maximal normal subgroup of | D3×D1439, C2×D4317, C3×D4317 |
| maximal quotient of | Dic4317, C2×D4317, D12951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8634, 3);