Finite Group DatabasebetaFinite Group Databasebeta| order | 19530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊#13049955) |
| unambiguous semidirect product | C5⋊(C3⋊#13049955) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C31 | C2×C3 |
| LCS | G ▷ C3×C5×C7×C31 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3255 |
Polycyclic presentation:
2,3^2,5,7,31|c^a=c^2,d^a=d^4,f^a=f^30,e^b=e^2,f^b=f^25570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19530, 183);