Finite Group DatabasebetaFinite Group Databasebeta| order | 8558 |
| automorphism | Aut(G) order 16602520 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4279 |
| unambiguous semidirect product | C11⋊D389 |
| unambiguous semidirect product | C389⋊D11 |
| Fitting, socle, derived, Hall | C11×C389 ⋊ C2 |
| Sylow | C389 ⋊ D11 |
| Sylow | C11 ⋊ D389 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C389 | C2 |
| LCS | G ▷ C11×C389 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,389|b^a=b^10,c^a=c^3882141 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D389, C2×D4279, C3×D4279, … |
| maximal normal subgroup of | D11×D389, C2×D4279, C3×D4279 |
| maximal quotient of | Dic4279, C2×D4279, C3×D4279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8558, 3);