Finite Group Databasebeta

← Group #13019832

Character table — Group #13019832

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444444810101010161616161616161616161616161616162020202040404040404040404040404040404040408080
order12222222445101010101010104444424101010101010202020202020202044444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111-1-111-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111-1-1-1-11111111111111111-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111-1-1-1-11111111111111111-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-11111111111-111111-1-1-1111111-1-1-1-1-1-1-1-111-111-1-111-1-111-1-111-1-11-1
χ10111111-1-11111111111-111111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-111-1-111-1-111-1-1111-1
χ11111111-1-11111111111-11111-11-1-1-1-1-1-111-1-11111-1-111-111-1-111-1-1-1-111-1-111-11
χ12111111-1-11111111111-11111-11-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-11111-1-111-1-1-11
χ13111111-1-11111111111-1-1-1-1-11-1-1-1111111-1-1-1-1-1-111-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ14111111-1-11111111111-1-1-1-1-11-1-1-1111111-1-1-1-1-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ15111111-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1111111-1-11ii−i−i−i−iii−i−iiiii−i−i1-1
χ16111111-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1111111-1-11−i−iiiii−i−iii−i−i−i−iii1-1
χ1722222222-2-222222222-2222200220000-2-2-2-2000022-2-2-2000000000000000000
χ1822222222-2-222222222-2-2-2-2-200220000-2-2-2-20000-2-2222000000000000000000
χ19222222-2-2-2-2222222222222200-2-20000-2-2220000-2-2-2-22000000000000000000
χ20222222-2-2-2-2222222222-2-2-2-200-2-20000-2-22200002222-2000000000000000000
χ212222-2-2002-222-2-222-2-2022-2-2000000002-2000000002-20002i−2i002i−2i0000000000
χ222222-2-2002-222-2-222-2-2022-2-2000000002-2000000002-2000−2i2i00−2i2i0000000000
χ232222-2-2002-222-2-222-2-20-2-222000000002-200000000-220002-200-220000000000
χ242222-2-2002-222-2-222-2-20-2-222000000002-200000000-22000-22002-20000000000
χ252222-2-200-2222-2-222-2-2022-2-200000000-2200000000-2202i−2i002i−2i000000000000
χ262222-2-200-2222-2-222-2-2022-2-200000000-2200000000-220−2i2i00−2i2i000000000000
χ272222-2-200-2222-2-222-2-20-2-22200000000-22000000002-202-200-22000000000000
χ282222-2-200-2222-2-222-2-20-2-22200000000-22000000002-20-22002-2000000000000
χ292-2-22-222-20022-2-2-2-22202-22-2002-20000000000002-200000000000i2−i2i2−i2i2−i2i2−i200
χ302-2-22-222-20022-2-2-2-22202-22-2002-20000000000002-200000000000−i2i2−i2i2−i2i2−i2i200
χ312-2-22-222-20022-2-2-2-2220-22-22002-2000000000000-22000000000002−22−2−22−2200
χ322-2-22-222-20022-2-2-2-2220-22-22002-2000000000000-2200000000000−22−222−22−200
χ332-2-22-22-220022-2-2-2-22202-22-200-22000000000000-2200000000000i2−i2−i2i2i2−i2−i2i200
χ342-2-22-22-220022-2-2-2-22202-22-200-22000000000000-2200000000000−i2i2i2−i2−i2i2i2−i200
χ352-2-22-22-220022-2-2-2-2220-22-2200-220000000000002-2000000000002−2−22−222−200
χ362-2-22-22-220022-2-2-2-2220-22-2200-220000000000002-200000000000−222−22−2−2200
χ374444444444-1-1-1-1-1-1-1-14000044-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ384444444444-1-1-1-1-1-1-1-140000-4-4-1-11111-1-1-1-1111100000000000000000000000
χ3944444444-4-4-1-1-1-1-1-1-1-1-4000000-1-155−5−5111155−5−500000000000000000000000
χ4044444444-4-4-1-1-1-1-1-1-1-1-4000000-1-1−5−5551111−5−55500000000000000000000000
χ41444444-4-444-1-1-1-1-1-1-1-1-400004-411-1-1-1-1-1-111111100000000000000000000000
χ42444444-4-444-1-1-1-1-1-1-1-1-40000-44111111-1-111-1-1-1-100000000000000000000000
χ43444444-4-4-4-4-1-1-1-1-1-1-1-140000001155−5−511-1-1−5−55500000000000000000000000
χ44444444-4-4-4-4-1-1-1-1-1-1-1-1400000011−5−55511-1-155−5−500000000000000000000000
χ454-4-444-400004444-4-4-4-404-4-44000000000000000000000000000000000000000
χ464-4-444-400004444-4-4-4-40-444-4000000000000000000000000000000000000000
χ478888-8-8008-8-2-222-2-2220000000000000-2200000000000000000000000000000
χ488888-8-800-88-2-222-2-22200000000000002-200000000000000000000000000000
χ4988-8-80000008-8008-80000000000000000000000000000000000000000000000
χ5088-8-8000000-2225−25-2225−250000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000000000
χ5188-8-8000000-2225−25-2225−25000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000000000
χ5288-8-8000000-22−2525-22−2525000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000000000
χ5388-8-8000000-22−2525-22−25250000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000000000
χ548-88-80000008-800-880000000000000000000000000000000000000000000000
χ558-88-8000000-2225−252-2−252500000000000000000−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000
χ568-88-8000000-2225−252-2−2525000000000000000002ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000
χ578-88-8000000-22−25252-225−25000000000000000002ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000
χ588-88-8000000-22−25252-225−2500000000000000000−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000
χ598-8-888-80000-2-2-2-222220000000000000002i5−2i5000000000000000000000000000
χ608-8-888-80000-2-2-2-22222000000000000000−2i52i5000000000000000000000000000
χ618-8-88-888-800-2-22222-2-20000000-2200000000000000000000000000000000000
χ628-8-88-88-8800-2-22222-2-200000002-200000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.