Finite Group DatabasebetaFinite Group Databasebeta| order | 34086 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D1311 |
| unambiguous semidirect product | C3⋊(C13×D437) |
| unambiguous semidirect product | C19⋊(C13×D69) |
| unambiguous semidirect product | C23⋊(C13×D57) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D1311 |
| commutator, cosocle, hypocenter | C3×C19×C23 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C19×C23 | C2 |
| LCS | G ▷ C3×C19×C23 | |
| UCS | C1 ◁ C13 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17043 |
8541 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34086, 16);