Finite Group DatabasebetaFinite Group Databasebeta| order | 20460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽32)⋊Dic11) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊Dic33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(ΓL(1,𝔽32)⋊D11) |
| commutator, hypocenter | C3×C11×C31 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C11×C31 | C2×C5 |
| prime radical | C2×C3×C11×ΓL(1,𝔽32) | C2 |
| LCS | G ▷ C3×C11×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4092 |
Polycyclic presentation:
2,3,5,11,31,2|a^2=f,b^a=b^2,d^a=d^10,e^a=e^30,e^c=e^16378 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20460, 66);