Finite Group DatabasebetaFinite Group Databasebeta| order | 3422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| affine general linear | AGL(1,𝔽59) |
| unambiguous semidirect product | D59⋊C29 |
| unambiguous semidirect product | (C59⋊C29)⋊C2 |
| Fitting, socle, derived, Sylow | C59 ⋊ C2×C29 |
| Hall | C59⋊C29 ⋊ C2 |
| Hall | D59 ⋊ C29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C59 | C2×C29 |
| LCS | G ▷ C59 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 59 |
Polycyclic presentation:
2,29,59|c^a=c^58,c^b=c^459 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3422, 1);