Finite Group DatabasebetaFinite Group Databasebeta| order | 34410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C31⋊C3)⋊C5)⋊D37 |
| unambiguous semidirect product | ((C31⋊C3)⋊D37)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C37 | C2×C3×C5 |
| LCS | G ▷ C31×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1147 |
Polycyclic presentation:
2,3,5,31,37|d^a=d^30,e^a=e^36,d^b=d^25,d^c=d^16337 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34410, 70);