# Group 144.3 downloaded from the LMFDB on 05 September 2026. 
 
## Various presentations of this group are stored in this file: 
#	 GPC is polycyclic presentation, GPerm is permutation group 
#	 GLZ, GLFp, GLZN, GLZq, GLFq if they exist are matrix groups 
 
# Many characteristics of the group are stored as booleans in a dict: 
#	 Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, 
#	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
#	 solvable, supersolvable 
 
# The character table is stored in the dict chartbl_n_i, where n is the 
# order of the group and i is which group of that order it is. The key 
# 'Irr' holds the table itself, as a matrix over the universal cyclotomic 
# field whose rows are the irreducible characters and whose columns are 
# the conjugacy classes, in the order given by 'ClassNames'. 

 
# Constructions 
# This uses Sage's interface to GAP, as Sage (currently) has no native support for PC groups
GPC = gap.new('PcGroupCode(2447562225994726176112,144)'); a = GPC.1; b = GPC.3; c = GPC.5;
GPerm = PermutationGroup(['(1,2,5)(3,7,10)(4,6,9)(8,11,12)(13,14,16,15,17,19,18,20,21)', '(13,15,18)(14,17,20)(16,19,21)', '(1,3)(2,6,7,11)(4,8)(5,9,10,12)', '(1,4,3,8)(2,7)(5,9,10,12)(6,11)', '(1,3)(4,8)(5,10)(9,12)', '(1,3)(2,7)(4,8)(6,11)'])
MS = MatrixSpace(GF(13), 3, 3)
GLFp = MatrixGroup([MS([[3, 2, 12], [0, 10, 7], [10, 2, 0]]), MS([[0, 10, 10], [8, 2, 5], [2, 11, 8]]), MS([[8, 0, 7], [9, 4, 6], [8, 0, 5]]), MS([[9, 0, 0], [0, 9, 0], [0, 0, 9]]), MS([[2, 0, 1], [5, 7, 12], [3, 0, 9]]), MS([[4, 7, 7], [3, 8, 10], [4, 9, 7]])])

 
# Booleans 
booleans_144_3 = {
    "Agroup": True,
    "Zgroup": False,
    "abelian": False,
    "almost_simple": False,
    "cyclic": False,
    "metabelian": True,
    "metacyclic": False,
    "monomial": True,
    "nilpotent": False,
    "perfect": False,
    "quasisimple": False,
    "rational": False,
    "solvable": True,
    "supersolvable": False
}

 
# Character Table 
UCF = UniversalCyclotomicField()
E = UCF.gen  # E(n) is the standard primitive n-th root of unity

chartbl_144_3 = {}
chartbl_144_3["Identifier"] = "144.3"
chartbl_144_3["Size"] = 144
chartbl_144_3["NrConjugacyClasses"] = 24
chartbl_144_3["ClassNames"] = ["1A", "2A", "3A1", "3A-1", "4A1", "4A-1", "4B1", "4B-1", "6A1", "6A-1", "9A1", "9A-1", "9A2", "9A-2", "9A4", "9A-4", "12A1", "12A-1", "12A5", "12A-5", "12B1", "12B-1", "12B5", "12B-5"]
chartbl_144_3["SizesCentralizers"] = [144, 48, 144, 144, 48, 48, 48, 48, 48, 48, 9, 9, 9, 9, 9, 9, 48, 48, 48, 48, 48, 48, 48, 48]
chartbl_144_3["OrderClassRepresentatives"] = [1, 2, 3, 3, 4, 4, 4, 4, 6, 6, 9, 9, 9, 9, 9, 9, 12, 12, 12, 12, 12, 12, 12, 12]
chartbl_144_3["ComputedPowerMaps"] = {2: [1, 1, 4, 3, 2, 2, 2, 2, 3, 4, 13, 14, 15, 16, 12, 11, 9, 10, 10, 9, 9, 10, 10, 9], 3: [1, 2, 1, 1, 6, 5, 8, 7, 2, 2, 3, 4, 4, 3, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8]}
chartbl_144_3["UnderlyingGroup"] = GPC
chartbl_144_3["ConjugacyClasses"] = [GPC.Identity(), c^2, a^3, a^6, c^3, c, b^2*c^3, b^2*c, a^6*c^2, a^3*c^2, a^4*b^2*c^2, a^5*c^2, a^8*c^2, a*b^2*c^2, a^7*b^2*c^2, a^2*c^2, a^3*c, a^6*c^3, a^6*c, a^3*c^3, a^3*b^2*c, a^6*b*c^2, a^6*b^2*c, a^3*b*c^2]
chartbl_144_3["Indicators"] = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
irr_144_3 = []
irr_144_3 += [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
irr_144_3 += [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(3)^-1, E(3), E(3), E(3)^-1, E(3)^-1, E(3), 1, 1, 1, 1, 1, 1, 1, 1]
irr_144_3 += [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), E(3), E(3)^-1, 1, 1, 1, 1, 1, 1, 1, 1]
irr_144_3 += [1, 1, E(9)^-3, E(9)^3, 1, 1, 1, 1, E(9)^3, E(9)^-3, E(9)^-4, E(9)^-2, E(9), E(9)^2, E(9)^-1, E(9)^4, E(9)^-3, E(9)^3, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3, E(9)^3, E(9)^-3]
irr_144_3 += [1, 1, E(9)^3, E(9)^-3, 1, 1, 1, 1, E(9)^-3, E(9)^3, E(9)^4, E(9)^2, E(9)^-1, E(9)^-2, E(9), E(9)^-4, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3]
irr_144_3 += [1, 1, E(9)^-3, E(9)^3, 1, 1, 1, 1, E(9)^3, E(9)^-3, E(9)^2, E(9), E(9)^4, E(9)^-1, E(9)^-4, E(9)^-2, E(9)^-3, E(9)^3, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3, E(9)^3, E(9)^-3]
irr_144_3 += [1, 1, E(9)^3, E(9)^-3, 1, 1, 1, 1, E(9)^-3, E(9)^3, E(9)^-2, E(9)^-1, E(9)^-4, E(9), E(9)^4, E(9)^2, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3]
irr_144_3 += [1, 1, E(9)^-3, E(9)^3, 1, 1, 1, 1, E(9)^3, E(9)^-3, E(9)^-1, E(9)^4, E(9)^-2, E(9)^-4, E(9)^2, E(9), E(9)^-3, E(9)^3, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3, E(9)^3, E(9)^-3]
irr_144_3 += [1, 1, E(9)^3, E(9)^-3, 1, 1, 1, 1, E(9)^-3, E(9)^3, E(9), E(9)^-4, E(9)^2, E(9)^4, E(9)^-2, E(9)^-1, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3, E(9)^3, E(9)^-3, E(9)^-3, E(9)^3]
irr_144_3 += [3, 3, 3, 3, -1, -1, -1, -1, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1]
irr_144_3 += [3, -1, 3, 3, -1-2*E(4), -1+2*E(4), 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1+2*E(4), -1-2*E(4), -1+2*E(4), -1-2*E(4), 1, 1, 1, 1]
irr_144_3 += [3, -1, 3, 3, -1+2*E(4), -1-2*E(4), 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1-2*E(4), -1+2*E(4), -1-2*E(4), -1+2*E(4), 1, 1, 1, 1]
irr_144_3 += [3, -1, 3, 3, 1, 1, -1-2*E(4), -1+2*E(4), -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1+2*E(4), -1-2*E(4), -1+2*E(4), -1-2*E(4)]
irr_144_3 += [3, -1, 3, 3, 1, 1, -1+2*E(4), -1-2*E(4), -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1-2*E(4), -1+2*E(4), -1-2*E(4), -1+2*E(4)]
irr_144_3 += [3, 3, 3*E(3)^-1, 3*E(3), -1, -1, -1, -1, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1]
irr_144_3 += [3, 3, 3*E(3), 3*E(3)^-1, -1, -1, -1, -1, 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3)]
irr_144_3 += [3, -1, -3*E(12)^2, 3*E(12)^4, -1-2*E(12)^3, -1+2*E(12)^3, 1, 1, -1*E(12)^4, E(12)^2, 0, 0, 0, 0, 0, 0, 2*E(12)+E(12)^2-2*E(12)^3, 1+2*E(12)-E(12)^2, 1-2*E(12)-E(12)^2, -2*E(12)+E(12)^2+2*E(12)^3, -1*E(12)^2, E(12)^4, E(12)^4, -1*E(12)^2]
irr_144_3 += [3, -1, 3*E(12)^4, -3*E(12)^2, -1+2*E(12)^3, -1-2*E(12)^3, 1, 1, E(12)^2, -1*E(12)^4, 0, 0, 0, 0, 0, 0, 1+2*E(12)-E(12)^2, 2*E(12)+E(12)^2-2*E(12)^3, -2*E(12)+E(12)^2+2*E(12)^3, 1-2*E(12)-E(12)^2, E(12)^4, -1*E(12)^2, -1*E(12)^2, E(12)^4]
irr_144_3 += [3, -1, -3*E(12)^2, 3*E(12)^4, -1+2*E(12)^3, -1-2*E(12)^3, 1, 1, -1*E(12)^4, E(12)^2, 0, 0, 0, 0, 0, 0, -2*E(12)+E(12)^2+2*E(12)^3, 1-2*E(12)-E(12)^2, 1+2*E(12)-E(12)^2, 2*E(12)+E(12)^2-2*E(12)^3, -1*E(12)^2, E(12)^4, E(12)^4, -1*E(12)^2]
irr_144_3 += [3, -1, 3*E(12)^4, -3*E(12)^2, -1-2*E(12)^3, -1+2*E(12)^3, 1, 1, E(12)^2, -1*E(12)^4, 0, 0, 0, 0, 0, 0, 1-2*E(12)-E(12)^2, -2*E(12)+E(12)^2+2*E(12)^3, 2*E(12)+E(12)^2-2*E(12)^3, 1+2*E(12)-E(12)^2, E(12)^4, -1*E(12)^2, -1*E(12)^2, E(12)^4]
irr_144_3 += [3, -1, -3*E(12)^2, 3*E(12)^4, 1, 1, -1-2*E(12)^3, -1+2*E(12)^3, -1*E(12)^4, E(12)^2, 0, 0, 0, 0, 0, 0, -1*E(12)^2, E(12)^4, E(12)^4, -1*E(12)^2, 2*E(12)+E(12)^2-2*E(12)^3, 1+2*E(12)-E(12)^2, 1-2*E(12)-E(12)^2, -2*E(12)+E(12)^2+2*E(12)^3]
irr_144_3 += [3, -1, 3*E(12)^4, -3*E(12)^2, 1, 1, -1+2*E(12)^3, -1-2*E(12)^3, E(12)^2, -1*E(12)^4, 0, 0, 0, 0, 0, 0, E(12)^4, -1*E(12)^2, -1*E(12)^2, E(12)^4, 1+2*E(12)-E(12)^2, 2*E(12)+E(12)^2-2*E(12)^3, -2*E(12)+E(12)^2+2*E(12)^3, 1-2*E(12)-E(12)^2]
irr_144_3 += [3, -1, -3*E(12)^2, 3*E(12)^4, 1, 1, -1+2*E(12)^3, -1-2*E(12)^3, -1*E(12)^4, E(12)^2, 0, 0, 0, 0, 0, 0, -1*E(12)^2, E(12)^4, E(12)^4, -1*E(12)^2, -2*E(12)+E(12)^2+2*E(12)^3, 1-2*E(12)-E(12)^2, 1+2*E(12)-E(12)^2, 2*E(12)+E(12)^2-2*E(12)^3]
irr_144_3 += [3, -1, 3*E(12)^4, -3*E(12)^2, 1, 1, -1-2*E(12)^3, -1+2*E(12)^3, E(12)^2, -1*E(12)^4, 0, 0, 0, 0, 0, 0, E(12)^4, -1*E(12)^2, -1*E(12)^2, E(12)^4, 1-2*E(12)-E(12)^2, -2*E(12)+E(12)^2+2*E(12)^3, 2*E(12)+E(12)^2-2*E(12)^3, 1+2*E(12)-E(12)^2]
chartbl_144_3["Irr"] = Matrix(UCF, 24, 24, irr_144_3)