Finite Group DatabasebetaFinite Group Databasebeta| order | 34140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#14556189 |
| unambiguous semidirect product | C3⋊(C5×#14556189) |
| Fitting, socle, Hall | C3×C5×C569 ⋊ C4 |
| derived, Hall | C3×C569 ⋊ C4×C5 |
| Hall | C5×C569 ⋊ Dic3 |
| Sylow | C569 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ #14556189 |
| Sylow | C3 ⋊ C5×#14556189 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#14556189 |
| commutator, hypocenter | C3×C569 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C569 | C4 |
| prime radical | C3×C5×D569 | C2 |
| cosocle | C3×D569 | C2×C5 |
| LCS | G ▷ C3×C569 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8535 |
2160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34140, 17);