Finite Group DatabasebetaFinite Group Databasebeta| order | 20460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #16811771⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C31 | C22×C5 |
| LCS | G ▷ C3×C11×C31 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1023 |
Polycyclic presentation:
2^2,5,3,11,31|f^a=f^30,d^b=d^2,e^b=e^10,e^c=e^4,f^c=f^1690 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20460, 129);