Finite Group DatabasebetaFinite Group Databasebeta| order | 722 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D19 |
| unambiguous semidirect product | C19⋊(C2×C19) |
| Fitting, socle, Sylow | C192 ⋊ C2 |
| derived | C19 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C192 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C19 | |
17 conjugacy classes of subgroups.
| transitive degree | μt(G) = 38 |
209 conjugacy classes — view the full character table.
| maximal subgroup of | D192, C2×C19×D19, C19×D19⋊C3, … |
| maximal normal subgroup of | D192, C2×C19×D19, C19×D19⋊C3, … |
| maximal quotient of | C19×Dic19, C2×C19×D19, C3×C19×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(722, 3);