Let p be a prime number, let G be a finite group, let N be a normal subgroup of G, and let \(\theta \) be a G-invariant irreducible character of N. In Rizo (J Algebra 514:254–272, 2018), we introduced a canonical partition of the set \(\mathrm{Irr}(G|\theta )\) of irreducible constituents of the induced character \(\theta ^G\), relative to the prime p. We call the elements of this partition the \(\theta \)-blocks. In this paper, we construct a canonical basis of the complex space of class functions defined on \(\{ x \in G \, |\, x_p \in N\}\), which supersedes previous non-canonical constructions. This allows us to define \(\theta \)-decomposition numbers in a natural way. We also prove that the elements of the partition of \({\text {Irr}}(G|\theta )\) established by these \(\theta \)-decomposition numbers are the \(\theta \)-blocks.

令p为素数，令G为有限群，令N为G的正规子群，令\（\ theta \）为N的G不变不可约性。在Rizo（J Algebra 514：254–272，2018）中，我们引入了诱导字符\（\ theta ^ G的不可约成分的集合\（\ mathrm {Irr}（G | \ theta）\）的规范划分\）相对于素数p。我们将此分区的元素称为\（\ theta \）- blocks。在本文中，我们构造了\（\ {x \ in G \，| \，x_p \ in N \} \）上定义的类函数的复杂空间的规范基础。，它取代了以前的非规范构造。这使我们可以自然地定义\（\ theta \）-分解数字。我们还证明了由这些\（\ theta \）分解数字建立的\（{\ text {Irr}}（G | \ theta）\）分区的元素是\（\ theta \）-块。