Finite Group DatabasebetaFinite Group Databasebeta| order | 34284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic2857⋊C3 |
| derived, Sylow | C2857 ⋊ C3×C4 |
| Hall | Dic2857 ⋊ C3 |
| Hall | C2857⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2857⋊C3 |
| commutator, hypocenter | C2857 | C3×C4 |
| Fitting, socle, cosocle | C2×C2857 | C2×C3 |
| prime radical | C2×C2857⋊C3 | C2 |
| LCS | G ▷ C2857 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11428 |
Polycyclic presentation:
2,3,2857,2|a^2=d,c^a=c^2856,c^b=c^2506964 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34284, 2);