Finite Group DatabasebetaFinite Group Databasebeta| order | 34314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C19⋊(D43⋊C7)) |
| unambiguous semidirect product | C19⋊(C3⋊(D43⋊C7)) |
| unambiguous semidirect product | (C43⋊C7)⋊D57 |
| unambiguous semidirect product | D2451⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C43 | C2×C7 |
| LCS | G ▷ C3×C19×C43 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2451 |
Polycyclic presentation:
2,3,7,19,43|b^a=b^2,d^a=d^18,e^a=e^42,e^c=e^41381 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34314, 41);