Finite Group DatabasebetaFinite Group Databasebeta| order | 7422 |
| automorphism | Aut(G) order 9173592 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3711 |
| unambiguous semidirect product | C3⋊D1237 |
| unambiguous semidirect product | C1237⋊D3 |
| Fitting, socle, derived, Hall | C3×C1237 ⋊ C2 |
| Sylow | C1237 ⋊ D3 |
| Sylow | C3 ⋊ D1237 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C1237 | C2 |
| LCS | G ▷ C3×C1237 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1237|b^a=b^2,c^a=c^12361857 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1237, C2×D3711, D11133, … |
| maximal normal subgroup of | D3×D1237, C2×D3711, C3⋊(D1237⋊C3), … |
| maximal quotient of | Dic3711, C2×D3711, D11133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7422, 5);