Finite Group DatabasebetaFinite Group Databasebeta| order | 19530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D315 |
| unambiguous semidirect product | C5⋊(C31×D63) |
| unambiguous semidirect product | C7⋊(C31×D45) |
| unambiguous semidirect product | C9⋊(C31×D35) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D315 |
| commutator, cosocle, hypocenter | C5×C7×C9 | C2×C31 |
| Frattini | C3 | C31×D105 |
| Fitting | C5×C7×C9×C31 | C2 |
| socle | C3×C5×C7×C31 | D3 |
| LCS | G ▷ C5×C7×C9 | |
| UCS | C1 ◁ C31 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9765 |
4929 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19530, 24);