Finite Group DatabasebetaFinite Group Databasebeta| order | 10806 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1801⋊C3 |
| unambiguous semidirect product | (C1801⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C1801 ⋊ C2×C3 |
| Hall | C1801⋊C3 ⋊ C2 |
| Hall | D1801 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1801 | C2×C3 |
| LCS | G ▷ C1801 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1801|c^a=c^1800,c^b=c^1727306 conjugacy classes — view the full character table.
| maximal subgroup of | #20297880⋊C3, C2×D1801⋊C3, #30633828⋊C2, … |
| maximal normal subgroup of | #20297880⋊C3, C2×D1801⋊C3, #30633828⋊C2, … |
| maximal quotient of | Dic1801⋊C3, C2×D1801⋊C3, #30633826⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10806, 1);