Finite Group DatabasebetaFinite Group Databasebeta| order | 19530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#16840862 |
| derived, Hall | C5×C7×C31 ⋊ C2×C9 |
| Hall | C5×#14519869 ⋊ C2 |
| Hall | D1085 ⋊ C9 |
| Hall | #14519869 ⋊ D5 |
| Hall | C7×C31 ⋊ C9×D5 |
| Hall | C5×C31 ⋊ D7⋊C9 |
| Hall | C5×C7 ⋊ D31⋊C9 |
| Sylow | C31 ⋊ C5⋊(D7⋊C9) |
| Sylow | C7 ⋊ C5⋊(D31⋊C9) |
| Sylow | C5 ⋊ #16840862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊#13049960 |
| commutator, hypocenter | C5×C7×C31 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C7×C31 | C2×C3 |
| prime radical | C3×D1085 | C3 |
| LCS | G ▷ C5×C7×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9765 |
Polycyclic presentation:
2,3,5,7,31,3|b^3=f,c^a=c^4,d^a=d^6,e^a=e^30,d^b=d^2,e^b=e^5576 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19530, 60);