Finite Group DatabasebetaFinite Group Databasebeta| order | 10554 |
| automorphism | Aut(G) order 18553932 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5277 |
| unambiguous semidirect product | C3⋊D1759 |
| unambiguous semidirect product | C1759⋊D3 |
| Fitting, socle, derived, Hall | C3×C1759 ⋊ C2 |
| Sylow | C1759 ⋊ D3 |
| Sylow | C3 ⋊ D1759 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C1759 | C2 |
| LCS | G ▷ C3×C1759 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1759|b^a=b^2,c^a=c^17582640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1759, C2×D5277, D15831, … |
| maximal normal subgroup of | D3×D1759, C2×D5277, C3⋊(D1759⋊C3), … |
| maximal quotient of | Dic5277, C2×D5277, D15831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10554, 5);