Finite Group DatabasebetaFinite Group Databasebeta| order | 19530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | D3×#10620253⋊C5 |
| unambiguous semidirect product | C3⋊(C2×#10620253⋊C5) |
| unambiguous semidirect product | (D3×#10620253)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C31 | C2×C3×C5 |
| LCS | G ▷ C3×C7×C31 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 651 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19530, 101);