Finite Group DatabasebetaFinite Group Databasebeta| order | 20748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D1729 |
| unambiguous semidirect product | (D3×C7)⋊D247 |
| unambiguous semidirect product | (D3×C13)⋊D133 |
| unambiguous semidirect product | (D3×C19)⋊D91 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C13×C19 | C22 |
| LCS | G ▷ C3×C7×C13×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5187 |
2598 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20748, 393);