Finite Group DatabasebetaFinite Group Databasebeta| order | 34220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C59⋊AGL(1,𝔽5))⋊C29 |
| unambiguous semidirect product | (C59⋊C29)⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C5×C59 ⋊ C4×C29 |
| Hall | C5×C59⋊C29 ⋊ C4 |
| Hall | C59⋊C29 ⋊ AGL(1,𝔽5) |
| Hall | C59⋊AGL(1,𝔽5) ⋊ C29 |
| Sylow | C59 ⋊ AGL(1,𝔽5)×C29 |
| Sylow | C5 ⋊ Dic59⋊C29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C59 | C4×C29 |
| prime radical | D5×C59⋊C29 | C2 |
| cosocle | D5×C59 | C2×C29 |
| LCS | G ▷ C5×C59 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 295 |
Polycyclic presentation:
2,29,2,5,59|a^2=c,d^a=d^2,e^a=e^58,e^b=e^4,d^c=d^4149 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34220, 14);