Finite Group DatabasebetaFinite Group Databasebeta| order | 1292 |
| isoclinism | isoclinic class of D17×D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D19 |
| unambiguous semidirect product | (C19×D17)⋊C2 |
| unambiguous semidirect product | (C17×D19)⋊C2 |
| unambiguous semidirect product | D323⋊C2 |
| Fitting, socle, derived, Hall | C17×C19 ⋊ C22 |
| Sylow | C19 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C19 | C22 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 323 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D17×D19⋊C3, C3×D17×D19, D19×D51, … |
| maximal normal subgroup of | D17×D19⋊C3, C3×D17×D19, C11×D17×D19, … |
| maximal quotient of | C3×D17×D19, D19×D51, D17×D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1292, 7);