![]() ![]() A finite group is monomial if every irreducible complex character is induced from a linear character of a subgroup. Return True if the groups are isomorphic. An elementary abelian group is a finite abelian group, where every nontrivial element has order \(p\), where \(p\) is a prime. Return True if this group is elementary abelian. Return a list of the irreducible characters of self. ![]() Return the permutation group that is the intersection of self and other. (Same as oup_id().) Return the ID code of this group, which is a list of two integers. Wraps HAP’s Homology function, written by Graham Ellis, applied to the \(p\)-Sylow subgroup of \(G\). Wraps HAP’s GroupHomology function, written by Graham Ellis.Ĭomputes the \(p\)-part of the group homology \(H_n(G, F)\), where \(F = \ZZ\) if \(p=0\) and \(F = \ZZ / p \ZZ\) if \(p > 0\) is a prime. The holomorph of a group as a permutation group.Ĭomputes the group homology \(H_n(G, F)\), where \(F = \ZZ\) if \(p=0\) and \(F = \ZZ / p \ZZ\) if \(p > 0\) is a prime. Return whether item is an element of this group - however ignores parentage. Return the index of this group in the GAP database of primitive groups. Return the ID code of this group, which is a list of two integers. Return tuple of generators of this group.įor this group, returns a generating set which has few elements. Return the i-th generator of self that is, the i-th element of the list self.gens(). domain() not moved by any element of self. Return the list of points fixed by self, i.e., the subset of. Return the underlying set that this permutation group acts on. Wraps GAP’s DirectProduct, Embedding, and Projection. Return the derived series of this group as a list of permutation groups. Return the degree of this permutation group. Return a list of the cosets of S in self. Return the group formed by conjugating self with g. Return a complete list of representatives of conjugacy classes of subgroups in a permutation group \(G\). Return a complete list of representatives of conjugacy classes in a permutation group \(G\). Return a list with all the conjugacy classes of self. Return the conjugacy class of g inside the group self. Return the composition series of this group as a list of permutation groups. Return the commutator subgroup of a group, or of a pair of groups. Return the matrix of values of the irreducible characters of a permutation group \(G\) at the conjugacy classes of \(G\).Ĭomputes the group cohomology \(H^n(G, F)\), where \(F = \ZZ\) if \(p=0\) and \(F = \ZZ / p \ZZ\) if \(p > 0\) is a prime.Ĭompute the p-part of the group cohomology \(H^n(G, F)\), where \(F = \ZZ\) if \(p=0\) and \(F = \ZZ / p \ZZ\) if \(p > 0\) is a prime. Return a group character from values, where values is a list of the values of the character evaluated on the conjugacy classes. Return the subgroup of elements that commute with every element of this group. Return the number of elements of this group. Return the list of block systems of imprimitivity. Return a finitely presented group isomorphic to self.
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