Finite Group DatabasebetaFinite Group Databasebeta| order | 8866 |
| automorphism | Aut(G) order 15958800 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4433 |
| unambiguous semidirect product | C11⋊D403 |
| unambiguous semidirect product | C13⋊D341 |
| unambiguous semidirect product | C31⋊D143 |
| Fitting, socle, derived, Hall | C11×C13×C31 ⋊ C2 |
| Hall | C13×C31 ⋊ D11 |
| Hall | C11×C31 ⋊ D13 |
| Hall | C11×C13 ⋊ D31 |
| Sylow | C31 ⋊ D143 |
| Sylow | C13 ⋊ D341 |
| Sylow | C11 ⋊ D403 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C13×C31 | C2 |
| LCS | G ▷ C11×C13×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,13,31|b^a=b^10,c^a=c^12,d^a=d^302218 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D143, D13×D341, D11×D403, … |
| maximal normal subgroup of | D31×D143, D13×D341, D11×D403, … |
| maximal quotient of | Dic4433, C2×D4433, C3×D4433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8866, 8);