Finite Group DatabasebetaFinite Group Databasebeta| order | 4506 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D751⋊C3 |
| unambiguous semidirect product | (C751⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C751 ⋊ C2×C3 |
| Hall | C751⋊C3 ⋊ C2 |
| Hall | D751 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C751 | C2×C3 |
| LCS | G ▷ C751 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 751 |
| transitive degree | μt(G) = 751 |
Polycyclic presentation:
2,3,751|c^a=c^750,c^b=c^678131 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D751⋊C3, C3⋊(D751⋊C3), C5×D751⋊C3, … |
| maximal normal subgroup of | C3×D751⋊C3, C5×D751⋊C3, (D751⋊C3)⋊C5, … |
| maximal quotient of | D751⋊C9, C3×D751⋊C3, C3⋊(D751⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4506, 1);