# Group 64.54 downloaded from the LMFDB on 11 October 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(309504273051162771967,64)'); a = GPC.1; b = GPC.2;
GPerm = PermutationGroup(['(1,34,2,33)(3,36,4,35)(5,38,6,37)(7,40,8,39)(9,42,10,41)(11,44,12,43)(13,46,14,45)(15,48,16,47)(17,50,18,49)(19,52,20,51)(21,54,22,53)(23,56,24,55)(25,58,26,57)(27,60,28,59)(29,62,30,61)(31,64,32,63)', '(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)(33,58,34,57)(35,60,36,59)(37,62,38,61)(39,64,40,63)(41,56,42,55)(43,53,44,54)(45,50,46,49)(47,52,48,51)', '(1,13,5,12,4,16,8,10,2,14,6,11,3,15,7,9)(17,25,23,31,19,27,22,30,18,26,24,32,20,28,21,29)(33,41,39,47,35,43,38,46,34,42,40,48,36,44,37,45)(49,61,53,60,52,64,56,58,50,62,54,59,51,63,55,57)', '(1,7,3,6,2,8,4,5)(9,15,11,14,10,16,12,13)(17,21,20,24,18,22,19,23)(25,29,28,32,26,30,27,31)(33,37,36,40,34,38,35,39)(41,45,44,48,42,46,43,47)(49,55,51,54,50,56,52,53)(57,63,59,62,58,64,60,61)', '(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15)(17,19,18,20)(21,23,22,24)(25,27,26,28)(29,31,30,32)(33,35,34,36)(37,39,38,40)(41,43,42,44)(45,47,46,48)(49,52,50,51)(53,56,54,55)(57,60,58,59)(61,64,62,63)', '(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)'])
MS = MatrixSpace(GF(31), 2, 2)
GLFp = MatrixGroup([MS([[29, 28], [30, 29]]), MS([[8, 28], [1, 23]])])

 
# Booleans 
booleans_64_54 = {
    "Agroup": False,
    "Zgroup": False,
    "abelian": False,
    "almost_simple": False,
    "cyclic": False,
    "metabelian": True,
    "metacyclic": True,
    "monomial": True,
    "nilpotent": True,
    "perfect": False,
    "quasisimple": False,
    "rational": False,
    "solvable": True,
    "supersolvable": True
}

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

chartbl_64_54 = {}
chartbl_64_54["Identifier"] = "64.54"
chartbl_64_54["Size"] = 64
chartbl_64_54["NrConjugacyClasses"] = 19
chartbl_64_54["ClassNames"] = ["1A", "2A", "4A", "4B", "4C", "8A1", "8A3", "16A1", "16A3", "16A5", "16A7", "32A1", "32A3", "32A5", "32A7", "32A9", "32A11", "32A13", "32A15"]
chartbl_64_54["SizesCentralizers"] = [64, 64, 32, 4, 4, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32]
chartbl_64_54["OrderClassRepresentatives"] = [1, 2, 4, 4, 4, 8, 8, 16, 16, 16, 16, 32, 32, 32, 32, 32, 32, 32, 32]
chartbl_64_54["ComputedPowerMaps"] = {2: [1, 1, 2, 2, 2, 3, 3, 6, 7, 7, 6, 8, 9, 10, 11, 11, 10, 9, 8]}
chartbl_64_54["UnderlyingGroup"] = GPC
chartbl_64_54["ConjugacyClasses"] = [GPC.Identity(), b^16, b^8, a*b^19, a*b^8, b^4, b^12, b^2, b^6, b^10, b^14, b, b^3, b^5, b^25, b^9, b^21, b^13, b^17]
chartbl_64_54["Indicators"] = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1]
irr_64_54 = []
irr_64_54 += [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
irr_64_54 += [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
irr_64_54 += [1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1]
irr_64_54 += [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1]
irr_64_54 += [2, 2, 2, 0, 0, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0]
irr_64_54 += [2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1]
irr_64_54 += [2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1]
irr_64_54 += [2, 2, -2, 0, 0, 0, 0, -1*E(16)^2-E(16)^-2, E(16)^2+E(16)^-2, E(16)^2+E(16)^-2, -1*E(16)^2-E(16)^-2, -1*E(16)^3-E(16)^-3, E(16)+E(16)^-1, -1*E(16)-E(16)^-1, E(16)^3+E(16)^-3, E(16)^3+E(16)^-3, -1*E(16)-E(16)^-1, E(16)+E(16)^-1, -1*E(16)^3-E(16)^-3]
irr_64_54 += [2, 2, -2, 0, 0, 0, 0, -1*E(16)^2-E(16)^-2, E(16)^2+E(16)^-2, E(16)^2+E(16)^-2, -1*E(16)^2-E(16)^-2, E(16)^3+E(16)^-3, -1*E(16)-E(16)^-1, E(16)+E(16)^-1, -1*E(16)^3-E(16)^-3, -1*E(16)^3-E(16)^-3, E(16)+E(16)^-1, -1*E(16)-E(16)^-1, E(16)^3+E(16)^-3]
irr_64_54 += [2, 2, -2, 0, 0, 0, 0, E(16)^2+E(16)^-2, -1*E(16)^2-E(16)^-2, -1*E(16)^2-E(16)^-2, E(16)^2+E(16)^-2, -1*E(16)-E(16)^-1, -1*E(16)^3-E(16)^-3, E(16)^3+E(16)^-3, E(16)+E(16)^-1, E(16)+E(16)^-1, E(16)^3+E(16)^-3, -1*E(16)^3-E(16)^-3, -1*E(16)-E(16)^-1]
irr_64_54 += [2, 2, -2, 0, 0, 0, 0, E(16)^2+E(16)^-2, -1*E(16)^2-E(16)^-2, -1*E(16)^2-E(16)^-2, E(16)^2+E(16)^-2, E(16)+E(16)^-1, E(16)^3+E(16)^-3, -1*E(16)^3-E(16)^-3, -1*E(16)-E(16)^-1, -1*E(16)-E(16)^-1, -1*E(16)^3-E(16)^-3, E(16)^3+E(16)^-3, E(16)+E(16)^-1]
irr_64_54 += [2, -2, 0, 0, 0, -1*E(32)^4-E(32)^-4, E(32)^4+E(32)^-4, -1*E(32)^6-E(32)^-6, E(32)^2+E(32)^-2, -1*E(32)^2-E(32)^-2, E(32)^6+E(32)^-6, -1*E(32)^5-E(32)^-5, E(32)+E(32)^-1, E(32)^7+E(32)^-7, E(32)^3+E(32)^-3, -1*E(32)^3-E(32)^-3, -1*E(32)^7-E(32)^-7, -1*E(32)-E(32)^-1, E(32)^5+E(32)^-5]
irr_64_54 += [2, -2, 0, 0, 0, -1*E(32)^4-E(32)^-4, E(32)^4+E(32)^-4, -1*E(32)^6-E(32)^-6, E(32)^2+E(32)^-2, -1*E(32)^2-E(32)^-2, E(32)^6+E(32)^-6, E(32)^5+E(32)^-5, -1*E(32)-E(32)^-1, -1*E(32)^7-E(32)^-7, -1*E(32)^3-E(32)^-3, E(32)^3+E(32)^-3, E(32)^7+E(32)^-7, E(32)+E(32)^-1, -1*E(32)^5-E(32)^-5]
irr_64_54 += [2, -2, 0, 0, 0, -1*E(32)^4-E(32)^-4, E(32)^4+E(32)^-4, E(32)^6+E(32)^-6, -1*E(32)^2-E(32)^-2, E(32)^2+E(32)^-2, -1*E(32)^6-E(32)^-6, -1*E(32)^3-E(32)^-3, E(32)^7+E(32)^-7, -1*E(32)-E(32)^-1, -1*E(32)^5-E(32)^-5, E(32)^5+E(32)^-5, E(32)+E(32)^-1, -1*E(32)^7-E(32)^-7, E(32)^3+E(32)^-3]
irr_64_54 += [2, -2, 0, 0, 0, -1*E(32)^4-E(32)^-4, E(32)^4+E(32)^-4, E(32)^6+E(32)^-6, -1*E(32)^2-E(32)^-2, E(32)^2+E(32)^-2, -1*E(32)^6-E(32)^-6, E(32)^3+E(32)^-3, -1*E(32)^7-E(32)^-7, E(32)+E(32)^-1, E(32)^5+E(32)^-5, -1*E(32)^5-E(32)^-5, -1*E(32)-E(32)^-1, E(32)^7+E(32)^-7, -1*E(32)^3-E(32)^-3]
irr_64_54 += [2, -2, 0, 0, 0, E(32)^4+E(32)^-4, -1*E(32)^4-E(32)^-4, -1*E(32)^2-E(32)^-2, -1*E(32)^6-E(32)^-6, E(32)^6+E(32)^-6, E(32)^2+E(32)^-2, -1*E(32)^7-E(32)^-7, E(32)^5+E(32)^-5, E(32)^3+E(32)^-3, -1*E(32)-E(32)^-1, E(32)+E(32)^-1, -1*E(32)^3-E(32)^-3, -1*E(32)^5-E(32)^-5, E(32)^7+E(32)^-7]
irr_64_54 += [2, -2, 0, 0, 0, E(32)^4+E(32)^-4, -1*E(32)^4-E(32)^-4, -1*E(32)^2-E(32)^-2, -1*E(32)^6-E(32)^-6, E(32)^6+E(32)^-6, E(32)^2+E(32)^-2, E(32)^7+E(32)^-7, -1*E(32)^5-E(32)^-5, -1*E(32)^3-E(32)^-3, E(32)+E(32)^-1, -1*E(32)-E(32)^-1, E(32)^3+E(32)^-3, E(32)^5+E(32)^-5, -1*E(32)^7-E(32)^-7]
irr_64_54 += [2, -2, 0, 0, 0, E(32)^4+E(32)^-4, -1*E(32)^4-E(32)^-4, E(32)^2+E(32)^-2, E(32)^6+E(32)^-6, -1*E(32)^6-E(32)^-6, -1*E(32)^2-E(32)^-2, -1*E(32)-E(32)^-1, -1*E(32)^3-E(32)^-3, E(32)^5+E(32)^-5, E(32)^7+E(32)^-7, -1*E(32)^7-E(32)^-7, -1*E(32)^5-E(32)^-5, E(32)^3+E(32)^-3, E(32)+E(32)^-1]
irr_64_54 += [2, -2, 0, 0, 0, E(32)^4+E(32)^-4, -1*E(32)^4-E(32)^-4, E(32)^2+E(32)^-2, E(32)^6+E(32)^-6, -1*E(32)^6-E(32)^-6, -1*E(32)^2-E(32)^-2, E(32)+E(32)^-1, E(32)^3+E(32)^-3, -1*E(32)^5-E(32)^-5, -1*E(32)^7-E(32)^-7, E(32)^7+E(32)^-7, E(32)^5+E(32)^-5, -1*E(32)^3-E(32)^-3, -1*E(32)-E(32)^-1]
chartbl_64_54["Irr"] = Matrix(UCF, 19, 19, irr_64_54)