Finite Group Databasebeta

← Group #13167602

Character table — Group #13167602

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444488888888888888888888181818181818181818181818181818181818181818181818181818181818181818181818727272727272727272727272
order12222236666666336666663366666666666666666644448888888812121212121212122424242424242424242424242424242444441212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ51111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ61111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ11222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ12222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000111111113333−3−3−3−33333−3−3−3−3000000000000
χ13222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000011111111−3−3−3−33333−3−3−3−33333000000000000
χ142222-2-2222-2-2-2-222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-222-200000000-2-22222-2-20000000000000000000000000000
χ152222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-1111111112-2-222222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000
χ162222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-1111111112-2-22-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1000000000000
χ172222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-222-20000000011-1-1-1-1113333−3−3−3−3−3−3−3−33333000000000000
χ182222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-222-20000000011-1-1-1-111−3−3−3−333333333−3−3−3−3000000000000
χ1922-2-22-222-222-2-2-22222-2-2-2-22222-2-222-2-2-2-22222-2-2-2-2000022−2−222−2−20000000022−2−222−2−222−2−222−2−2000000000000
χ2022-2-22-222-222-2-2-22222-2-2-2-22222-2-222-2-2-2-22222-2-2-2-20000−2−222−2−22200000000−2−222−2−222−2−222−2−222000000000000
χ2122-2-22-2-1-11-1-11112222-2-2-2-2-1-122-2-2-1-11111-1-1-1-11111000022−2−222−2−23−333−3−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ2222-2-22-2-1-11-1-11112222-2-2-2-2-1-122-2-2-1-11111-1-1-1-11111000022−2−222−2−2−33−3−333−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ2322-2-22-2-1-11-1-11112222-2-2-2-2-1-122-2-2-1-11111-1-1-1-111110000−2−222−2−2223−333−3−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ2422-2-22-2-1-11-1-11112222-2-2-2-2-1-122-2-2-1-11111-1-1-1-111110000−2−222−2−222−33−3−333−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ2522-2-2-2222-2-2-222-22222-2-2-2-222-2-22222-2-2-2-2-2-2-2-22222000022−2−2−2−2220000000022−2−222−2−2−2−222−2−222000000000000
χ2622-2-2-2222-2-2-222-22222-2-2-2-222-2-22222-2-2-2-2-2-2-2-222220000−2−22222−2−200000000−2−222−2−22222−2−222−2−2000000000000
χ2722-2-2-22-1-1111-1-112222-2-2-2-2-1-1-2-222-1-111111111-1-1-1-1000022−2−2−2−2223−3−3−3333−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ2822-2-2-22-1-1111-1-112222-2-2-2-2-1-1-2-222-1-111111111-1-1-1-1000022−2−2−2−222−3333−3−3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ2922-2-2-22-1-1111-1-112222-2-2-2-2-1-1-2-222-1-111111111-1-1-1-10000−2−22222−2−23−3−3−3333−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3022-2-2-22-1-1111-1-112222-2-2-2-2-1-1-2-222-1-111111111-1-1-1-10000−2−22222−2−2−3333−3−3−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ312-22-2002-220000-222-2-222-2-2220000-2-222-2-20000000002i−2i02−22−2−i2i2−i2i2002i−2i2i−2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ322-22-2002-220000-222-2-222-2-2220000-2-222-2-20000000002i−2i0−22−22i2−i2i2−i2002i−2i2i−2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ332-22-2002-220000-222-2-222-2-2220000-2-222-2-2000000000−2i2i02−22−2i2−i2i2−i200−2i2i−2i2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ342-22-2002-220000-222-2-222-2-2220000-2-222-2-2000000000−2i2i0−22−22−i2i2−i2i200−2i2i−2i2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ352-22-200-11-1−i3i3−i3i3122-2-222-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i302i−2i02−22−2−i2i2−i2i23−3−ii−ii−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ362-22-200-11-1−i3i3−i3i3122-2-222-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i302i−2i0−22−22i2−i2i2−i23−3−ii−ii−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ372-22-200-11-1−i3i3−i3i3122-2-222-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i30−2i2i02−22−2i2−i2i2−i2−33i−ii−i3−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ382-22-200-11-1−i3i3−i3i3122-2-222-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i30−2i2i0−22−22−i2i2−i2i2−33i−ii−i3−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ392-22-200-11-1i3−i3i3−i3122-2-222-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i302i−2i02−22−2−i2i2−i2i2−33−ii−ii3−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ402-22-200-11-1i3−i3i3−i3122-2-222-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i302i−2i0−22−22i2−i2i2−i2−33−ii−ii3−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ412-22-200-11-1i3−i3i3−i3122-2-222-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i30−2i2i02−22−2i2−i2i2−i23−3i−ii−i−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ422-22-200-11-1i3−i3i3−i3122-2-222-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i30−2i2i0−22−22−i2i2−i2i23−3i−ii−i−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ432-2-22002-2-20000222-2-2-2-222220000-2-2-2-22200000000200-200002i−2i−2i2i220000-2-2000000002i−2i−2i2i2i−2i−2i2i000000000000
χ442-2-22002-2-20000222-2-2-2-222220000-2-2-2-22200000000200-20000−2i2i2i−2i220000-2-200000000−2i2i2i−2i−2i2i2i−2i000000000000
χ452-2-22002-2-20000222-2-2-2-222220000-2-2-2-22200000000-20022-2-220000-2-20000222-2-222-2-2200000000000000000000
χ462-2-22002-2-20000222-2-2-2-222220000-2-2-2-22200000000-2002-222-20000-2-2000022-222-2-222-200000000000000000000
χ472-2-2200-111−i3i3i3−i3-122-2-2-2-222-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3200-200002i−2i−2i2i-1-1−i3i3i3−i3113−3−33−333−3−iii−i−iii−i000000000000
χ482-2-2200-111−i3i3i3−i3-122-2-2-2-222-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3200-20000−2i2i2i−2i-1-1−i3i3i3−i311−333−33−3−33i−i−iii−i−ii000000000000
χ492-2-2200-111−i3i3i3−i3-122-2-2-2-222-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3-20022-2-22000011i3−i3−i3i3-1-1-111-1-111-1−i3i3i3−i3i3−i3−i3i3000000000000
χ502-2-2200-111−i3i3i3−i3-122-2-2-2-222-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3-2002-222-2000011i3−i3−i3i3-1-11-1-111-1-11i3−i3−i3i3−i3i3i3−i3000000000000
χ512-2-2200-111i3−i3−i3i3-122-2-2-2-222-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3200-200002i−2i−2i2i-1-1i3−i3−i3i311−333−33−3−33−iii−i−iii−i000000000000
χ522-2-2200-111i3−i3−i3i3-122-2-2-2-222-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3200-20000−2i2i2i−2i-1-1i3−i3−i3i3113−3−33−333−3i−i−iii−i−ii000000000000
χ532-2-2200-111i3−i3−i3i3-122-2-2-2-222-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3-20022-2-22000011−i3i3i3−i3-1-1-111-1-111-1i3−i3−i3i3−i3i3i3−i3000000000000
χ542-2-2200-111i3−i3−i3i3-122-2-2-2-222-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3-2002-222-2000011−i3i3i3−i3-1-11-1-111-1-11−i3i3i3−i3i3−i3−i3i3000000000000
χ55444444444444441-21-21-21-21-21-21-21-21-21-21-21-21-21-200000000000000000000000000000000000002020000-1-1-1-1
χ56444444444444441-21-21-21-21-21-21-21-21-21-21-21-21-21-20000000000000000000000000000000000000-20-200001111
χ5744444444444444-21-21-21-21-21-21-21-21-21-21-21-21-21-210000000000000000000000000000000000002020-1-1-1-10000
χ5844444444444444-21-21-21-21-21-21-21-21-21-21-21-21-21-21000000000000000000000000000000000000-20-2011110000
χ594444-4-4444-4-4-4-441-21-21-21-21-2-12-121-21-21-2-12-12-12-12000000000000000000000000000000000000020-20000-1-111
χ604444-4-4444-4-4-4-441-21-21-21-21-2-12-121-21-21-2-12-12-12-120000000000000000000000000000000000000-202000011-1-1
χ614444-4-4444-4-4-4-44-21-21-21-21-212-12-1-21-21-212-12-12-12-100000000000000000000000000000000000020-20-1-1110000
χ624444-4-4444-4-4-4-44-21-21-21-21-212-12-1-21-21-212-12-12-12-1000000000000000000000000000000000000-202011-1-10000
χ6344-4-44-444-444-4-4-41-21-2-12-121-21-2-121-2-12-121-21-2-12-12000000000000000000000000000000000000000000003−33−3
χ6444-4-44-444-444-4-4-41-21-2-12-121-21-2-121-2-12-121-21-2-12-1200000000000000000000000000000000000000000000−33−33
χ6544-4-44-444-444-4-4-4-21-212-12-1-21-212-1-212-12-1-21-212-12-100000000000000000000000000000000000000003−33−30000
χ6644-4-44-444-444-4-4-4-21-212-12-1-21-212-1-212-12-1-21-212-12-10000000000000000000000000000000000000000−33−330000
χ6744-4-4-4444-4-4-444-41-21-2-12-121-2-121-21-2-12-12-12-121-21-2000000000000000000000000000000000000000000003−3−33
χ6844-4-4-4444-4-4-444-41-21-2-12-121-2-121-21-2-12-12-12-121-21-200000000000000000000000000000000000000000000−333−3
χ6944-4-4-4444-4-4-444-4-21-212-12-1-212-1-21-212-12-12-12-1-21-2100000000000000000000000000000000000000003−3−330000
χ7044-4-4-4444-4-4-444-4-21-212-12-1-212-1-21-212-12-12-12-1-21-210000000000000000000000000000000000000000−333−30000
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χ898-8-8800-4444i3−4i3−4i34i3-42-4-24-242-4-1200001-21-2-12i3−2i3−i32i3−i32i3i3−2i3000000000000000000000000000000000000000000000000
χ908-8-8800-4444i3−4i3−4i34i3-4-424-24-2-422-10000-21-212-1−2i3i32i3−i32i3−i3−2i3i3000000000000000000000000000000000000000000000000

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