Finite Group DatabasebetaFinite Group Databasebeta| order | 4506 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C751⋊C3 |
| unambiguous semidirect product | (C2×C751)⋊C3 |
| Fitting, socle, Hall | C2×C751 ⋊ C3 |
| derived, Sylow | C751 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C751⋊C3 |
| commutator, cosocle, hypocenter | C751 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C751 | C3 |
| LCS | G ▷ C751 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 753 |
| transitive degree | μt(G) = 1502 |
506 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C751⋊C3, C2×C3×C751⋊C3, C2×C5×C751⋊C3, … |
| maximal normal subgroup of | C2×C3×C751⋊C3, C2×C5×C751⋊C3, C2×(C751⋊C3)⋊C5, … |
| maximal quotient of | C2×C751⋊C9, D3×C751⋊C3, C2×C3×C751⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4506, 2);