Finite Group DatabasebetaFinite Group Databasebeta| order | 4518 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C251 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C251 |
| unambiguous semidirect product | C3⋊(C2×C3×C251) |
| Fitting, socle, Hall | C32×C251 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C251 |
| Sylow | C32 ⋊ C2×C251 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C251 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C3×C251 |
| Frattini | C1 | G |
| Fitting, socle | C32×C251 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C251 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 257 |
| transitive degree | μt(G) = 1506 |
2259 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C251⋊C5, C3×C5×D3×C251, C3×D15×C251, … |
| maximal normal subgroup of | C3×D3×C251⋊C5, C3×C5×D3×C251, C3×D3×C7×C251 |
| maximal quotient of | C3×C5×D3×C251, C3×D15×C251, C3⋊AGL(1,𝔽7)×C251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4518, 7);