/* Group 23276.b downloaded from the LMFDB on 16 August 2026. */ /* Various presentations of this group are stored in this file: GPC is polycyclic presentation GPerm is permutation group GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups Many characteristics of the group are stored as booleans in a record: Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable The character table is stored as chartbl_n_i where n is the order of the group and i is which group of that order it is. Conjugacy classes are stored in the variable 'C' with elements from the group 'G'. */ /* Constructions */ GPC := PCGroup([5, -2, -2, -11, -23, 23, 10, 21722, 97717, 32563, 9688, 79873, 238704, 278309, 56939]); a,b,c,d := Explode([GPC.1, GPC.3, GPC.4, GPC.5]); AssignNames(~GPC, ["a", "a2", "b", "c", "d"]); GPerm := PermutationGroup< 46 | (1,45,15,26)(2,42,14,29)(3,39,13,32)(4,36,12,35)(5,33,11,38)(6,30,10,41)(7,27,9,44)(8,24)(16,46,23,25)(17,43,22,28)(18,40,21,31)(19,37,20,34), (1,38,23,39)(2,37,22,40)(3,36,21,41)(4,35,20,42)(5,34,19,43)(6,33,18,44)(7,32,17,45)(8,31,16,46)(9,30,15,24)(10,29,14,25)(11,28,13,26)(12,27) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_23276_b := rec< RF | Agroup := true, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false>; /* Character Table */ G:= GPC; C := SequenceToConjugacyClasses([car |< 1, 1, Id(G)>,< 2, 529, a^2*c^3*d>,< 4, 5819, a^3*b*c^8*d^2>,< 4, 5819, a*b*c^15*d^11>,< 11, 1058, b^2*c^21*d^22>,< 11, 1058, b^4*c^17*d^5>,< 11, 1058, b^6*c^9*d^21>,< 11, 1058, b^8*c^16*d^9>,< 11, 1058, b^10*c^7*d^9>,< 22, 1058, a^2*b*c*d^9>,< 22, 1058, a^2*b^3*d^6>,< 22, 1058, a^2*b^5*c^21*d^2>,< 22, 1058, a^2*b^7*c^17*d^18>,< 22, 1058, a^2*b^9*c^9*d^16>,< 23, 44, d>,< 23, 44, c>,< 23, 44, c^2>,< 23, 44, c^3>,< 23, 44, c^4>,< 23, 44, c^5>,< 23, 44, c^6>,< 23, 44, c^7>,< 23, 44, c^8>,< 23, 44, c^9>,< 23, 44, c^10>,< 23, 44, c^11>]); CR := CharacterRing(G); x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(4: Sparse := true); S := [ K |1,-1,-1*K.1,K.1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(4: Sparse := true); S := [ K |1,-1,K.1,-1*K.1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,2,0,0,K.1^5+K.1^-5,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^5+K.1^-5,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,2,0,0,K.1^4+K.1^-4,K.1^3+K.1^-3,K.1+K.1^-1,K.1^5+K.1^-5,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^5+K.1^-5,K.1+K.1^-1,K.1^3+K.1^-3,K.1^4+K.1^-4,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,2,0,0,K.1^3+K.1^-3,K.1^5+K.1^-5,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1^5+K.1^-5,K.1^3+K.1^-3,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,2,0,0,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^5+K.1^-5,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^5+K.1^-5,K.1^4+K.1^-4,K.1^2+K.1^-2,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^4+K.1^-4,K.1^5+K.1^-5,K.1^5+K.1^-5,K.1^4+K.1^-4,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,-2,0,0,K.1^5+K.1^-5,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^5-K.1^-5,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := -1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,-2,0,0,K.1^4+K.1^-4,K.1^3+K.1^-3,K.1+K.1^-1,K.1^5+K.1^-5,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^5-K.1^-5,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^4-K.1^-4,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := -1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,-2,0,0,K.1^3+K.1^-3,K.1^5+K.1^-5,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^5-K.1^-5,-1*K.1^3-K.1^-3,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := -1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,-2,0,0,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^5+K.1^-5,K.1^3+K.1^-3,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^5-K.1^-5,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := -1; x`IsIrreducible := true; K := CyclotomicField(11: Sparse := true); S := [ K |2,-2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^4+K.1^-4,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,-1*K.1^4-K.1^-4,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,2,2,2,2,2,2,2,2,2,2,2,2]; x := CR!S; x`IsCharacter := true; x`Schur := -1; x`IsIrreducible := true; x := CR!\[44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(23: Sparse := true); S := [ K |44,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2-2*K.1^2-2*K.1^3-4*K.1^5-4*K.1^6-2*K.1^7-2*K.1^8-2*K.1^9-K.1^10-4*K.1^11-4*K.1^-11-K.1^-10-2*K.1^-9-2*K.1^-8-2*K.1^-7-4*K.1^-6-4*K.1^-5-2*K.1^-3-2*K.1^-2,2+4*K.1^2+3*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+2*K.1^7+4*K.1^8+2*K.1^9+2*K.1^-9+4*K.1^-8+2*K.1^-7+2*K.1^-6+2*K.1^-5+2*K.1^-4+3*K.1^-3+4*K.1^-2,2*K.1^3-2*K.1^5+K.1^7-2*K.1^8-2*K.1^10+2*K.1^11+2*K.1^-11-2*K.1^-10-2*K.1^-8+K.1^-7-2*K.1^-5+2*K.1^-3,2+4*K.1^4+2*K.1^5+3*K.1^6+4*K.1^7+2*K.1^8+2*K.1^9+2*K.1^10+2*K.1^11+2*K.1^-11+2*K.1^-10+2*K.1^-9+2*K.1^-8+4*K.1^-7+3*K.1^-6+2*K.1^-5+4*K.1^-4,-2*K.1^2+2*K.1^3+K.1^4+2*K.1^5-2*K.1^7-2*K.1^9-2*K.1^-9-2*K.1^-7+2*K.1^-5+K.1^-4+2*K.1^-3-2*K.1^-2,-2-2*K.1^2-4*K.1^3-2*K.1^4-2*K.1^5-4*K.1^7-2*K.1^8-K.1^9-4*K.1^10-2*K.1^11-2*K.1^-11-4*K.1^-10-K.1^-9-2*K.1^-8-4*K.1^-7-2*K.1^-5-2*K.1^-4-4*K.1^-3-2*K.1^-2,-1-K.1^2-K.1^3-3*K.1^4+K.1^5-K.1^6+K.1^7-3*K.1^8-K.1^9-K.1^10-3*K.1^11-3*K.1^-11-K.1^-10-K.1^-9-3*K.1^-8+K.1^-7-K.1^-6+K.1^-5-3*K.1^-4-K.1^-3-K.1^-2,-2*K.1^2-2*K.1^4-2*K.1^6+2*K.1^8+2*K.1^9+K.1^11+K.1^-11+2*K.1^-9+2*K.1^-8-2*K.1^-6-2*K.1^-4-2*K.1^-2,2+3*K.1^2+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^6+4*K.1^9+4*K.1^10+2*K.1^11+2*K.1^-11+4*K.1^-10+4*K.1^-9+2*K.1^-6+2*K.1^-5+2*K.1^-4+2*K.1^-3+3*K.1^-2,-2*K.1^4-2*K.1^5+2*K.1^6+K.1^8-2*K.1^9+2*K.1^10+2*K.1^-10-2*K.1^-9+K.1^-8+2*K.1^-6-2*K.1^-5-2*K.1^-4,2*K.1^2-2*K.1^3+K.1^5-2*K.1^6-2*K.1^9+2*K.1^11+2*K.1^-11-2*K.1^-9-2*K.1^-6+K.1^-5-2*K.1^-3+2*K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; _ := CharacterTable(G : Check := 0); chartbl_23276_b:= KnownIrreducibles(CR);