Finite Group DatabasebetaFinite Group Databasebeta| order | 4506 |
| automorphism | Aut(G) order 3379500 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2253 |
| unambiguous semidirect product | C3⋊D751 |
| unambiguous semidirect product | C751⋊D3 |
| Fitting, socle, derived, Hall | C3×C751 ⋊ C2 |
| Sylow | C751 ⋊ D3 |
| Sylow | C3 ⋊ D751 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C751 | C2 |
| LCS | G ▷ C3×C751 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 754 |
| transitive degree | μt(G) = 2253 |
Polycyclic presentation:
2,3,751|b^a=b^2,c^a=c^7501128 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D6759, C3⋊(D751⋊C3), C3⋊D2253, … |
| maximal normal subgroup of | C3⋊(D751⋊C3), C3×D2253, C5×D2253, … |
| maximal quotient of | D6759, C3⋊D2253, C3×D2253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4506, 5);