Finite Group DatabasebetaFinite Group Databasebeta| order | 7942 |
| automorphism | Aut(G) order 13580820 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3971 |
| unambiguous semidirect product | C11⋊D361 |
| unambiguous semidirect product | C361⋊D11 |
| Fitting, derived, Hall | C11×C361 ⋊ C2 |
| Sylow | C361 ⋊ D11 |
| Sylow | C11 ⋊ D361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C11×C361 | C2 |
| Frattini | C19 | D209 |
| socle | C11×C19 | D19 |
| LCS | G ▷ C11×C361 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,19^2|c^19=d^18,b^a=b^10,c^a=c^18d,d^a=d^181987 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D361, C2×D3971, C11⋊(D361⋊C3), … |
| maximal normal subgroup of | D11×D361, C2×D3971, C11⋊(D361⋊C3), … |
| maximal quotient of | Dic3971, C2×D3971, C3×D3971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7942, 4);