Finite Group DatabasebetaFinite Group Databasebeta| order | 20862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×C3⋊(D19⋊C3) |
| unambiguous semidirect product | C3⋊(C61×D19⋊C3) |
| unambiguous semidirect product | (C19⋊C3)⋊(D3×C61) |
| unambiguous semidirect product | D57⋊(C3×C61) |
| Fitting, socle | C3×C19×C61 ⋊ C2×C3 |
| derived | C3×C19 ⋊ C2×C3×C61 |
| Hall | C3×C19⋊C3×C61 ⋊ C2 |
| Hall | C19×C61 ⋊ C3×D3 |
| Hall | C3×C19⋊C3 ⋊ C2×C61 |
| Sylow | C19 ⋊ C3×D3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C3⋊(D19⋊C3) |
| commutator, cosocle, hypocenter | C3×C19 | C2×C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C61 | C2×C3 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C61 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3477 |
1098 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20862, 56);