Finite Group DatabasebetaFinite Group Databasebeta| order | 4518 |
| automorphism | Aut(G) order 3388500 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2259 |
| unambiguous semidirect product | C9⋊D251 |
| unambiguous semidirect product | C251⋊D9 |
| Fitting, derived, Hall | C9×C251 ⋊ C2 |
| Sylow | C251 ⋊ D9 |
| Sylow | C9 ⋊ D251 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C251 | C2 |
| Frattini | C3 | D753 |
| socle | C3×C251 | D3 |
| LCS | G ▷ C9×C251 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 260 |
| transitive degree | μt(G) = 2259 |
Polycyclic presentation:
2,3,251,3|b^3=d^2,b^a=b^2d,c^a=c^250,d^a=d^21131 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D2259, D11295, C9⋊(D251⋊C5), … |
| maximal normal subgroup of | C5×D2259, C9⋊(D251⋊C5), C7×D2259 |
| maximal quotient of | C5×D2259, D11295, C7×D2259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4518, 4);