Finite Group DatabasebetaFinite Group Databasebeta| order | 20742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C3457⋊C3 |
| unambiguous semidirect product | (C2×C3457)⋊C3 |
| Fitting, socle, Hall | C2×C3457 ⋊ C3 |
| derived, Sylow | C3457 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3457⋊C3 |
| commutator, cosocle, hypocenter | C3457 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3457 | C3 |
| LCS | G ▷ C3457 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6914 |
2310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20742, 2);