Finite Group DatabasebetaFinite Group Databasebeta| order | 4566 |
| automorphism | Aut(G) order 3470160 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2283 |
| unambiguous semidirect product | C3⋊D761 |
| unambiguous semidirect product | C761⋊D3 |
| Fitting, socle, derived, Hall | C3×C761 ⋊ C2 |
| Sylow | C761 ⋊ D3 |
| Sylow | C3 ⋊ D761 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C761 | C2 |
| LCS | G ▷ C3×C761 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 764 |
| transitive degree | μt(G) = 2283 |
Polycyclic presentation:
2,3,761|b^a=b^2,c^a=c^7601143 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D6849, C3⋊D2283, C3×D2283, … |
| maximal normal subgroup of | C3×D2283, C5×D2283, C3⋊(D761⋊C5), … |
| maximal quotient of | D6849, C3⋊D2283, C3×D2283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4566, 3);