Finite Group DatabasebetaFinite Group Databasebeta| order | 20460 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | Dic11×(C31⋊C3)⋊C5 |
| unambiguous semidirect product | (Dic11×ΓL(1,𝔽32))⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D11×(C31⋊C3)⋊C5 |
| commutator, hypocenter | C11×C31 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C11×C31 | C2×C3×C5 |
| prime radical | C2×C11×(C31⋊C3)⋊C5 | C2 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1364 |
238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20460, 85);