Finite Group Databasebeta

← Group #13167496

Character table — Group #13167496

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444488888888888888888888181818181818181818181818181818181818181818181818181818181818181818181818727272727272727272727272
order1222344666121212123366666633666666121212121212121212121212224466668888888812121212242424242424242424242424242424242244666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000
χ1022222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200000000-2-2-2-20000000000000000000000000000
χ112222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ122222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ132222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211110000000011113333−3−3−3−33333−3−3−3−3000000000000
χ142222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111000000001111−3−3−3−33333−3−3−3−33333000000000000
χ152222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-2-1-1-1-10000000011113333−3−3−3−3−3−3−3−33333000000000000
χ162222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-2-1-1-1-1000000001111−3−3−3−333333333−3−3−3−3000000000000
χ172222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-22211112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000
χ182222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2221111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ1922-2-222i−2i2-2-22i2i−2i−2i2222-2-2-2-22222-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000022−2−2−i2−i2i2i2000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ2022-2-222i−2i2-2-22i2i−2i−2i2222-2-2-2-22222-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000−2−222i2i2−i2−i20000−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ2122-2-22−2i2i2-2-2−2i−2i2i2i2222-2-2-2-22222-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000022−2−2i2i2−i2−i2000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ2222-2-22−2i2i2-2-2−2i−2i2i2i2222-2-2-2-22222-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i00000000−2−222−i2−i2i2i20000−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ2322-2-2-12i−2i-111−i−iii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii0000−i3−i3i3i322−2−2−i2−i2i2i23−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ2422-2-2-12i−2i-111−i−iii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii0000−i3−i3i3i3−2−222i2i2−i2−i23−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ2522-2-2-12i−2i-111−i−iii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii0000i3i3−i3−i322−2−2−i2−i2i2i2−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ2622-2-2-12i−2i-111−i−iii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii0000i3i3−i3−i3−2−222i2i2−i2−i2−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ2722-2-2-1−2i2i-111ii−i−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i0000−i3−i3i3i322−2−2i2i2−i2−i2−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ2822-2-2-1−2i2i-111ii−i−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i0000−i3−i3i3i3−2−222−i2−i2i2i2−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ2922-2-2-1−2i2i-111ii−i−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i0000i3i3−i3−i322−2−2i2i2−i2−i23−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ3022-2-2-1−2i2i-111ii−i−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i0000i3i3−i3−i3−2−222−i2−i2i2i23−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ312-22-2200-2-22000022-2-222-2-222-2-2-2-222000000000000002-2000000002i−2i2i−2i22-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000
χ322-22-2200-2-22000022-2-222-2-222-2-2-2-222000000000000002-200000000−2i2i−2i2i22-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000
χ332-22-2200-2-22000022-2-222-2-222-2-2-2-22200000000000000-2200002-22-20000-2-2222-22-22-22-200000000000000000000
χ342-22-2200-2-22000022-2-222-2-222-2-2-2-22200000000000000-220000-22-220000-2-222-22-22-22-2200000000000000000000
χ352-22-2-10011-1−i3i3−i3i322-2-222-2-2-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3002-2−i3i3−i3i300002i−2i2i−2i-1-1113−33−3−33−33−ii−ii−ii−ii000000000000
χ362-22-2-10011-1−i3i3−i3i322-2-222-2-2-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3002-2−i3i3−i3i30000−2i2i−2i2i-1-111−33−333−33−3i−ii−ii−ii−i000000000000
χ372-22-2-10011-1−i3i3−i3i322-2-222-2-2-1-11111-1-10000−i3−i3i3i3−i3−i3i3i300-22i3−i3i3−i32-22-2000011-1-1-11-11-11-11−i3i3−i3i3i3−i3i3−i3000000000000
χ382-22-2-10011-1−i3i3−i3i322-2-222-2-2-1-11111-1-10000−i3−i3i3i3−i3−i3i3i300-22i3−i3i3−i3-22-22000011-1-11-11-11-11-1i3−i3i3−i3−i3i3−i3i3000000000000
χ392-22-2-10011-1i3−i3i3−i322-2-222-2-2-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3002-2i3−i3i3−i300002i−2i2i−2i-1-111−33−333−33−3−ii−ii−ii−ii000000000000
χ402-22-2-10011-1i3−i3i3−i322-2-222-2-2-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3002-2i3−i3i3−i30000−2i2i−2i2i-1-1113−33−3−33−33i−ii−ii−ii−i000000000000
χ412-22-2-10011-1i3−i3i3−i322-2-222-2-2-1-11111-1-10000i3i3−i3−i3i3i3−i3−i300-22−i3i3−i3i32-22-2000011-1-1-11-11-11-11i3−i3i3−i3−i3i3−i3i3000000000000
χ422-22-2-10011-1i3−i3i3−i322-2-222-2-2-1-11111-1-10000i3i3−i3−i3i3i3−i3−i300-22−i3i3−i3i3-22-22000011-1-11-11-11-11-1−i3i3−i3i3i3−i3i3−i3000000000000
χ432-2-22200-22-2000022-2-2-2-22222-2-222-2-20000000000002-2002-2-222−2−22−222−200002−2−222−2−22−222−2−222−2000000000000
χ442-2-22200-22-2000022-2-2-2-22222-2-222-2-20000000000002-2002-2-22−222−22−2−220000−222−2−222−22−2−222−2−22000000000000
χ452-2-22200-22-2000022-2-2-2-22222-2-222-2-2000000000000-2200-222-22−2−222−2−2200002−2−222−2−222−2−222−2−22000000000000
χ462-2-22200-22-2000022-2-2-2-22222-2-222-2-2000000000000-2200-222-2−222−2−222−20000−222−2−222−2−222−2−222−2000000000000
χ472-2-22-1001-113−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−3332-200-111-12−2−22−222−23−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ482-2-22-1001-113−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−3332-200-111-1−222−22−2−223−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ492-2-22-1001-113−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−333-22001-1-112−2−222−2−22−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ502-2-22-1001-113−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−333-22001-1-11−222−2−222−2−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ512-2-22-1001-11−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−32-200-111-12−2−22−222−2−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ522-2-22-1001-11−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−32-200-111-1−222−22−2−22−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ532-2-22-1001-11−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−3-22001-1-112−2−222−2−223−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
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χ55444444444444441-21-21-21-21-21-21-21-21-21-21-21-21-21-2000000000000000000000000000000000000020200-1-100-1-1
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χ858-8-88800-88-800002-4-24-242-42-4-242-4-24000000000000000000000000000000000000000000000000000000000000
χ868-8-88800-88-80000-424-24-2-42-424-2-424-2000000000000000000000000000000000000000000000000000000000000
χ878-8-88-4004-4443−43−43432-4-24-242-4-121-2-121-200003−23−323−3233−23000000000000000000000000000000000000000000000000
χ888-8-88-4004-4443−43−4343-424-24-2-422-1-212-1-210000−23323−323−3−233000000000000000000000000000000000000000000000000
χ898-8-88-4004-44−434343−432-4-24-242-4-121-2-121-20000−3233−233−23−323000000000000000000000000000000000000000000000000
χ908-8-88-4004-44−434343−43-424-24-2-422-1-212-1-21000023−3−233−23323−3000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.