Finite Group DatabasebetaFinite Group Databasebeta| order | 10506 |
| automorphism | Aut(G) order 17145792 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5253 |
| unambiguous semidirect product | C3⋊D1751 |
| unambiguous semidirect product | C17⋊D309 |
| unambiguous semidirect product | C103⋊D51 |
| Fitting, socle, derived, Hall | C3×C17×C103 ⋊ C2 |
| Hall | C17×C103 ⋊ D3 |
| Hall | C3×C103 ⋊ D17 |
| Sylow | C103 ⋊ D51 |
| Hall | C3×C17 ⋊ D103 |
| Sylow | C17 ⋊ D309 |
| Sylow | C3 ⋊ D1751 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C103 | C2 |
| LCS | G ▷ C3×C17×C103 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,103|b^a=b^2,c^a=c^16,d^a=d^1022628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D103, D17×D309, D3×D1751, … |
| maximal normal subgroup of | D51×D103, D17×D309, D3×D1751, … |
| maximal quotient of | Dic5253, C2×D5253, D15759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10506, 11);