Finite Group DatabasebetaFinite Group Databasebeta| order | 20742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D3457⋊C3 |
| unambiguous semidirect product | (C3457⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C3457 ⋊ C2×C3 |
| Hall | C3457⋊C3 ⋊ C2 |
| Hall | D3457 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3457 | C2×C3 |
| LCS | G ▷ C3457 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3457 |
Polycyclic presentation:
2,3,3457|c^a=c^3456,c^b=c^722582 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20742, 1);