Finite Group DatabasebetaFinite Group Databasebeta| order | 15540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊#10625191) |
| unambiguous semidirect product | C7⋊(C3⋊#10625191) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C37 | C4 |
| prime radical, cosocle | C3×C7×D185 | C2 |
| LCS | G ▷ C3×C5×C7×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3885 |
Polycyclic presentation:
2^2,3,5,7,37|a^2=b,c^a=c^2,d^a=d^2,e^a=e^6,f^a=f^31,d^b=d^4,f^b=f^36990 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15540, 186);