Finite Group DatabasebetaFinite Group Databasebeta| order | 6942 |
| automorphism | Aut(G) order 7330752 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3471 |
| unambiguous semidirect product | C3⋊D1157 |
| unambiguous semidirect product | C13⋊D267 |
| unambiguous semidirect product | C89⋊D39 |
| Fitting, socle, derived, Hall | C3×C13×C89 ⋊ C2 |
| Hall | C13×C89 ⋊ D3 |
| Hall | C3×C89 ⋊ D13 |
| Sylow | C89 ⋊ D39 |
| Hall | C3×C13 ⋊ D89 |
| Sylow | C13 ⋊ D267 |
| Sylow | C3 ⋊ D1157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C89 | C2 |
| LCS | G ▷ C3×C13×C89 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,89|b^a=b^2,c^a=c^12,d^a=d^881737 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D39×D89, D13×D267, D3×D1157, … |
| maximal normal subgroup of | D39×D89, D13×D267, D3×D1157, … |
| maximal quotient of | Dic3471, C2×D3471, D10413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6942, 9);