Finite Group DatabasebetaFinite Group Databasebeta| order | 10538 |
| automorphism | Aut(G) order 25185820 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5269 |
| unambiguous semidirect product | C11⋊D479 |
| unambiguous semidirect product | C479⋊D11 |
| Fitting, socle, derived, Hall | C11×C479 ⋊ C2 |
| Sylow | C479 ⋊ D11 |
| Sylow | C11 ⋊ D479 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C479 | C2 |
| LCS | G ▷ C11×C479 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,479|b^a=b^10,c^a=c^4782636 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D479, C2×D5269, C3×D5269, … |
| maximal normal subgroup of | D11×D479, C2×D5269, C3×D5269 |
| maximal quotient of | Dic5269, C2×D5269, C3×D5269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10538, 3);