Finite Group DatabasebetaFinite Group Databasebeta| order | 7386 |
| automorphism | Aut(G) order 9084780 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3693 |
| unambiguous semidirect product | C3⋊D1231 |
| unambiguous semidirect product | C1231⋊D3 |
| Fitting, socle, derived, Hall | C3×C1231 ⋊ C2 |
| Sylow | C1231 ⋊ D3 |
| Sylow | C3 ⋊ D1231 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C1231 | C2 |
| LCS | G ▷ C3×C1231 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1231|b^a=b^2,c^a=c^12301848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1231, C2×D3693, D11079, … |
| maximal normal subgroup of | D3×D1231, C2×D3693, C3⋊(D1231⋊C3), … |
| maximal quotient of | Dic3693, C2×D3693, D11079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7386, 5);