Finite Group DatabasebetaFinite Group Databasebeta| order | 3534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D31 |
| Fitting, socle, derived, Hall | C19×C31 ⋊ C2×C3 |
| Hall | C31×C19⋊C3 ⋊ C2 |
| Hall | D589 ⋊ C3 |
| Hall | C19⋊C3 ⋊ D31 |
| Sylow | C31 ⋊ D19⋊C3 |
| Sylow | C19 ⋊ C3×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C31 | C2×C3 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 589 |
Polycyclic presentation:
2,3,19,31|c^a=c^18,d^a=d^30,c^b=c^7144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3534, 22);