Finite Group DatabasebetaFinite Group Databasebeta| order | 11566 |
| automorphism | Aut(G) order 33437306 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5783 |
| unambiguous semidirect product | C5783⋊C2 |
| Fitting, socle, derived, Sylow | C5783 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5783 | C2 |
| LCS | G ▷ C5783 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5783|b^a=b^57822893 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5783, C3×D5783, D17349 |
| maximal normal subgroup of | C2×D5783, C3×D5783 |
| maximal quotient of | Dic5783, C2×D5783, C3×D5783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11566, 1);