Finite Group DatabasebetaFinite Group Databasebeta| order | 7714 |
| automorphism | Aut(G) order 11663568 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3857 |
| unambiguous semidirect product | C7⋊D551 |
| unambiguous semidirect product | C19⋊D203 |
| unambiguous semidirect product | C29⋊D133 |
| Fitting, socle, derived, Hall | C7×C19×C29 ⋊ C2 |
| Hall | C19×C29 ⋊ D7 |
| Hall | C7×C29 ⋊ D19 |
| Hall | C7×C19 ⋊ D29 |
| Sylow | C29 ⋊ D133 |
| Sylow | C19 ⋊ D203 |
| Sylow | C7 ⋊ D551 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C19×C29 | C2 |
| LCS | G ▷ C7×C19×C29 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,19,29|b^a=b^6,c^a=c^18,d^a=d^281930 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D133, D19×D203, D7×D551, … |
| maximal normal subgroup of | D29×D133, D19×D203, D7×D551, … |
| maximal quotient of | Dic3857, C2×D3857, C3×D3857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7714, 9);