Finite Group DatabasebetaFinite Group Databasebeta| order | 34068 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C167⋊#595 |
| unambiguous semidirect product | C167⋊(C3×#595) |
| Fitting, socle, Hall | C3×C17×C167 ⋊ C4 |
| derived, Hall | C17×C167 ⋊ C3×C4 |
| Hall | C3×C167 ⋊ #595 |
| Sylow | C167 ⋊ C3×#595 |
| Hall | C3×C17 ⋊ Dic167 |
| Sylow | C17 ⋊ C3×Dic167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C167⋊#595 |
| commutator, hypocenter | C17×C167 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C167 | C4 |
| prime radical | C3×D17×C167 | C2 |
| cosocle | D17×C167 | C2×C3 |
| LCS | G ▷ C17×C167 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8517 |
2514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34068, 11);