Finite Group DatabasebetaFinite Group Databasebeta| order | 35340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #16812975⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C19×C31 | C22×C3 |
| LCS | G ▷ C5×C19×C31 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2945 |
Polycyclic presentation:
2^2,3,5,19,31|e^a=e^18,f^a=f^30,d^b=d^4,e^b=e^18,e^c=e^7,f^c=f^25281 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35340, 136);