Finite Group DatabasebetaFinite Group Databasebeta| order | 4518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D753 |
| unambiguous semidirect product | C251⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C251 ⋊ C2 |
| Sylow | C251 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D251 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C251 | C2 |
| LCS | G ▷ C32×C251 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2259 |
Polycyclic presentation:
2,3^2,251|b^a=b^2,c^a=c^2,d^a=d^2501131 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊(C3⋊(D251⋊C5)), C5×C3⋊D753, C3⋊D3765, … |
| maximal normal subgroup of | C3⋊(C3⋊(D251⋊C5)), C5×C3⋊D753, C7×C3⋊D753 |
| maximal quotient of | C5×C3⋊D753, C3⋊D3765, C7×C3⋊D753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4518, 10);