Finite Group DatabasebetaFinite Group Databasebeta| order | 37740 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #27160385⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C37 | C3×C4 |
| prime radical | C5×C17⋊(D37⋊C3) | C2 |
| cosocle | C5×D629 | C2×C3 |
| LCS | G ▷ C5×C17×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3145 |
Polycyclic presentation:
2,3,2,5,17,37|a^2=c,d^a=d^4,e^a=e^13,f^a=f^6,f^b=f^26,e^c=e^16,f^c=f^36339 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37740, 52);