Finite Group DatabasebetaFinite Group Databasebeta| order | 4518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D753 |
| unambiguous semidirect product | C3⋊(C3×D251) |
| unambiguous semidirect product | C251⋊(C3×D3) |
| Fitting, socle, Hall | C32×C251 ⋊ C2 |
| derived | C3×C251 ⋊ C2×C3 |
| Sylow | C251 ⋊ C3×D3 |
| Sylow | C32 ⋊ D251 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D753 |
| commutator, cosocle, hypocenter | C3×C251 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C251 | C2 |
| LCS | G ▷ C3×C251 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 257 |
| transitive degree | μt(G) = 1506 |
1134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C3⋊(D251⋊C5), C3×C5×D753, C3×D3765, … |
| maximal normal subgroup of | C3×C3⋊(D251⋊C5), C3×C5×D753, C3×C7×D753 |
| maximal quotient of | C3×C5×D753, C3×D3765, C3⋊(ΓL(1,𝔽8)⋊D251), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4518, 8);