Finite Group DatabasebetaFinite Group Databasebeta| order | 8214 |
| automorphism | Aut(G) order 10941048 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4107 |
| unambiguous semidirect product | C3⋊D1369 |
| unambiguous semidirect product | C1369⋊D3 |
| Fitting, derived, Hall | C3×C1369 ⋊ C2 |
| Sylow | C1369 ⋊ D3 |
| Sylow | C3 ⋊ D1369 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C1369 | C2 |
| Frattini | C37 | D111 |
| socle | C3×C37 | D37 |
| LCS | G ▷ C3×C1369 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,37^2|c^37=d^36,b^a=b^2,c^a=c^36d,d^a=d^362055 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1369, C2×D4107, D12321, … |
| maximal normal subgroup of | D3×D1369, C2×D4107, C3⋊(D1369⋊C3), … |
| maximal quotient of | Dic4107, C2×D4107, D12321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8214, 6);