Finite Group DatabasebetaFinite Group Databasebeta| order | 34220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C59⋊C29 |
| unambiguous semidirect product | (Dic5×C59)⋊C29 |
| derived, Hall | C5×C59 ⋊ C4×C29 |
| Hall | C5×C59⋊C29 ⋊ C4 |
| Hall | Dic5×C59 ⋊ C29 |
| Sylow | C59 ⋊ Dic5×C29 |
| Sylow | C5 ⋊ C4×C59⋊C29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×C59⋊C29 |
| 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 |
248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34220, 11);