Finite Group DatabasebetaFinite Group Databasebeta| order | 34220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic295⋊C29 |
| unambiguous semidirect product | (C59⋊C29)⋊Dic5 |
| derived, Hall | C5×C59 ⋊ C4×C29 |
| Hall | C5×C59⋊C29 ⋊ C4 |
| Hall | C59⋊C29 ⋊ Dic5 |
| Hall | Dic295 ⋊ C29 |
| Sylow | C59 ⋊ Dic5×C29 |
| Sylow | C5 ⋊ Dic59⋊C29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊AGL(1,𝔽59) |
| commutator, hypocenter | C5×C59 | C4×C29 |
| Fitting, socle, cosocle | C2×C5×C59 | C2×C29 |
| prime radical | C2×C5×C59⋊C29 | C2 |
| LCS | G ▷ C5×C59 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1180 |
Polycyclic presentation:
2,5,29,59,2|a^2=e,b^a=b^4,d^a=d^58,d^c=d^4242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34220, 12);