Finite Group DatabasebetaFinite Group Databasebeta| order | 10758 |
| automorphism | Aut(G) order 17427960 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5379 |
| unambiguous semidirect product | C3⋊D1793 |
| unambiguous semidirect product | C11⋊D489 |
| unambiguous semidirect product | C163⋊D33 |
| Fitting, socle, derived, Hall | C3×C11×C163 ⋊ C2 |
| Hall | C11×C163 ⋊ D3 |
| Hall | C3×C163 ⋊ D11 |
| Sylow | C163 ⋊ D33 |
| Hall | C3×C11 ⋊ D163 |
| Sylow | C11 ⋊ D489 |
| Sylow | C3 ⋊ D1793 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C163 | C2 |
| LCS | G ▷ C3×C11×C163 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,163|b^a=b^2,c^a=c^10,d^a=d^1622691 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D33×D163, D11×D489, D3×D1793, … |
| maximal normal subgroup of | D33×D163, D11×D489, D3×D1793, … |
| maximal quotient of | Dic5379, C2×D5379, D16137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10758, 9);