Finite Group DatabasebetaFinite Group Databasebeta| order | 34220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊AGL(1,𝔽59) |
| unambiguous semidirect product | (C2×C5)⋊AGL(1,𝔽59) |
| unambiguous semidirect product | (C2×D295)⋊C29 |
| unambiguous semidirect product | (C2×C59⋊C29)⋊D5 |
| Fitting, socle | C2×C5×C59 ⋊ C2×C29 |
| derived, Hall | C5×C59 ⋊ C22×C29 |
| Hall | C5×C59⋊C29 ⋊ C22 |
| Hall | C59⋊C29 ⋊ C2×D5 |
| Hall | C2×D295 ⋊ C29 |
| Sylow | C59 ⋊ C2×D5×C29 |
| Sylow | C5 ⋊ C2×AGL(1,𝔽59) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊AGL(1,𝔽59) |
| commutator, cosocle, hypocenter | C5×C59 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C59 | C2×C29 |
| LCS | G ▷ C5×C59 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 590 |
242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34220, 18);