Finite Group DatabasebetaFinite Group Databasebeta| order | 15922 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D419⋊C19 |
| unambiguous semidirect product | (C419⋊C19)⋊C2 |
| Fitting, socle, derived, Sylow | C419 ⋊ C2×C19 |
| Hall | C419⋊C19 ⋊ C2 |
| Hall | D419 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C419 | C2×C19 |
| LCS | G ▷ C419 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 419 |
Polycyclic presentation:
2,19,419|c^a=c^418,c^b=c^11449 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D419⋊C19 |
| maximal normal subgroup of | C2×D419⋊C19 |
| maximal quotient of | Dic419⋊C19, C2×D419⋊C19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15922, 1);