Finite Group Databasebeta

← Group #13155887

Character table — Group #13155887

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222222222444444444444444444444444668888888888121212121212121212121212121212121212121212121212121212121212121212121224242424242424242436363636363636367272727272108108
order122233344666666666121212123336666666661212121212121212121212124436661212121212122666666668812121212121212122424242424242424242424242424242441212121212121212228824242424466121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ71111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200222222220000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222222222200-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ11222222-122222-1-122-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-100000000022000000002222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1220000000-1-10000
χ12222222-122222-1-122-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-100000000022000000002222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-20000000110000
χ13222222-122222-1-122-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-1000000000-2-200000000-2-2-2-2111111111111222-1-1-1-1-1-1-2-20000000110000
χ14222222-122222-1-122-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-1000000000-2-200000000-2-2-2-2111111111111-2-2-2111111220000000-1-10000
χ1522222-122222-1222-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10022-1-1-1-1-1-100000000000000002-1-122-1-1-1-100000000200-1-100
χ1622222-122222-1222-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10022-1-1-1-1-1-10000000000000000-211-2-2111100000000-2001100
χ1722222-122222-1222-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-2-2-211111100-2-211111100000000000000002-1-122-1-1-1-100000000-2001100
χ1822222-122222-1222-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-2-2-211111100-2-21111110000000000000000-211-2-2111100000000200-1-100
χ1922222-12-2-222-1222-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-2-2-21111110022-1-1-1-1-1-100000000000000000−i3i300−i3−i3i3i300000000000−i3i300
χ2022222-12-2-222-1222-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-2-2-21111110022-1-1-1-1-1-100000000000000000i3−i300i3i3−i3−i300000000000i3−i300
χ2122222-12-2-222-1222-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111222-1-1-1-1-1-100-2-211111100000000000000000−i3i300−i3−i3i3i300000000000i3−i300
χ2222222-12-2-222-1222-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111222-1-1-1-1-1-100-2-211111100000000000000000i3−i300i3i3−i3−i300000000000−i3i300
χ232222-12222-1-1222-1222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000022-1-1-1-10000000
χ242222-12222-1-1222-1222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-1-2-2-1-122-1-1-1-11111-2-2-2-21111111100000000000-2-211110000000
χ252222-12222-1-1222-1222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-211-2-211112211-2-21111-1-1-1-12222-1-1-1-1-1-1-1-100000000000-2-211110000000
χ262222-12222-1-1222-1222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-211-2-21111-2-211-2-211111111-2-2-2-2111111110000000000022-1-1-1-10000000
χ272222-122-2-2-1-1222-12221111-12-1-1-12-1-1-12-12-2-2-2111111-21122-1-1-1-1-2-21111-211-2-2111100-1-122-1-1-1-133−3−300003333−3−3−3−3000000000000033−3−30000000
χ282222-122-2-2-1-1222-12221111-12-1-1-12-1-1-12-12-2-2-2111111-21122-1-1-1-1-2-21111-211-2-2111100-1-122-1-1-1-1−3−3330000−3−3−3−333330000000000000−3−3330000000
χ292222-122-2-2-1-1222-12221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-1-1-1-1-2-211112-1-122-1-1-1-10011-2-2111133−3−300003333−3−3−3−30000000000000−3−3330000000
χ302222-122-2-2-1-1222-12221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-1-1-1-1-2-211112-1-122-1-1-1-10011-2-21111−3−3330000−3−3−3−33333000000000000033−3−30000000
χ312-22-2222002-2-2-2-2-222-200002222-2-22-2-2-2-220000000000002i−2i22-2-20000000000000002−22i−2i2i−2i2i2i−2i−2i2−22−222−2−222−2−222−2−200000000000−i2i2−i2i2−i2i20000000
χ322-22-2222002-2-2-2-2-222-200002222-2-22-2-2-2-220000000000002i−2i22-2-2000000000000000−222i−2i2i−2i2i2i−2i−2i−22−22−2−222−2−222−2−22200000000000i2−i2i2−i2i2−i20000000
χ332-22-2222002-2-2-2-2-222-200002222-2-22-2-2-2-22000000000000−2i2i22-2-20000000000000002−2−2i2i−2i2i−2i−2i2i2i2−22−222−2−222−2−222−2−200000000000i2−i2i2−i2i2−i20000000
χ342-22-2222002-2-2-2-2-222-200002222-2-22-2-2-2-22000000000000−2i2i22-2-2000000000000000−22−2i2i−2i2i−2i−2i2i2i−22−22−2−222−2−222−2−22200000000000−i2i2−i2i2−i2i20000000
χ352-22-2-12200-11-2-2-2122-23−33−3-12-1-11-2-111-2120003−333−3−303−32i−2i-1-1110033−3−30−i3i300−i3−i3i3i32−2−ii2i−2i−i−iiiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000
χ362-22-2-12200-11-2-2-2122-23−33−3-12-1-11-2-111-2120003−333−3−303−32i−2i-1-1110033−3−30−i3i300−i3−i3i3i3−22−ii2i−2i−i−iii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000
χ372-22-2-12200-11-2-2-2122-23−33−3-12-1-11-2-111-2120003−333−3−303−3−2i2i-1-1110033−3−30i3−i300i3i3−i3−i32−2i−i−2i2iii−i−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000
χ382-22-2-12200-11-2-2-2122-23−33−3-12-1-11-2-111-2120003−333−3−303−3−2i2i-1-1110033−3−30i3−i300i3i3−i3−i3−22i−i−2i2iii−i−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000
χ392-22-2-12200-11-2-2-2122-2−33−33-12-1-11-2-111-212000−33−3−3330−332i−2i-1-11100−3−3330i3−i300i3i3−i3−i32−2−ii2i−2i−i−iiiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000
χ402-22-2-12200-11-2-2-2122-2−33−33-12-1-11-2-111-212000−33−3−3330−332i−2i-1-11100−3−3330i3−i300i3i3−i3−i3−22−ii2i−2i−i−iii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000
χ412-22-2-12200-11-2-2-2122-2−33−33-12-1-11-2-111-212000−33−3−3330−33−2i2i-1-11100−3−3330−i3i300−i3−i3i3i32−2i−i−2i2iii−i−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000
χ422-22-2-12200-11-2-2-2122-2−33−33-12-1-11-2-111-212000−33−3−3330−33−2i2i-1-11100−3−3330−i3i300−i3−i3i3i3−22i−i−2i2iii−i−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000
χ432-2-222222-2-2-2-2-222-2-2222-2-2222-2-2-2-2-2222-2-22-2-2-22-22-2222002-2-222-22-22-20000000000000000000000000000000000000000000000000000000002-2
χ442-2-222222-2-2-2-2-222-2-2222-2-2222-2-2-2-2-2222-2-22-2-2-22-22-2222002-2-222-22-22-2000000000000000000000000000000000000000000000000000000000-22
χ452-2-22222-22-2-2-2-222-2-22-2-222222-2-2-2-2-2222-22-2222-22-22-2-2-2002-2-22-22-22-22000000000000000000000000000000000000000000002-200000002-20000
χ462-2-22222-22-2-2-2-222-2-22-2-222222-2-2-2-2-2222-22-2222-22-22-2-2-2002-2-22-22-22-2200000000000000000000000000000000000000000000-220000000-220000
χ472-2-2222-1-22-2-2-21-12-212-2-222-1-12111-2-2-1-121-1-22-1-1-22-2211100-111-11-11-11-1000000000000000000000003−33−33−33−33−33−30003−33−33−32-20000000-110000
χ482-2-2222-1-22-2-2-21-12-212-2-222-1-12111-2-2-1-121-1-22-1-1-22-2211100-111-11-11-11-1000000000000000000000003−33−33−33−33−33−3000−33−33−33-2200000001-10000
χ492-2-2222-1-22-2-2-21-12-212-2-222-1-12111-2-2-1-121-1-22-1-1-22-2211100-111-11-11-11-100000000000000000000000−33−33−33−33−33−330003−33−33−3-2200000001-10000
χ502-2-2222-1-22-2-2-21-12-212-2-222-1-12111-2-2-1-121-1-22-1-1-22-2211100-111-11-11-11-100000000000000000000000−33−33−33−33−33−33000−33−33−332-20000000-110000
χ51444444-2-4-4444-2-244-24-4-4-4-4-2-24-2-2-244-2-24-22-4-422-4-4-4-422200-2-2-2-222222200000000000000000000000000000000000000000000000000000000000
χ5244444-2-24444-2-2-24-2-2-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-2001111111111000000000000000000000000000000000004-2-2-2-21111000000000000000
χ5344444-2-24444-2-2-24-2-2-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-200111111111100000000000000000000000000000000000-42222-1-1-1-1000000000000000
χ5444444-2-2-4-444-2-2-24-2-2-2-4-4-4-4-21-2-2-21-2-2-21-21222222222222001111-1-1-1-1-1-1000000000000000000000000000000000000−2i32i300i3i3−i3−i3000000000000000
χ5544444-2-2-4-444-2-2-24-2-2-2-4-4-4-4-21-2-2-21-2-2-21-21222222222222001111-1-1-1-1-1-10000000000000000000000000000000000002i3−2i300−i3−i3i3i3000000000000000
χ564444-24-244-2-24-2-2-24-24-2-2-2-21-2-211-2-2-21-2-2-2-24411-2-2-2-2-211001111-2-211110000000004400000000-2-2-2-2-2-2-2-211111111000000000000000000000000
χ574444-24-244-2-24-2-2-24-24-2-2-2-21-2-211-2-2-21-2-2-2-24411-2-2-2-2-211001111-2-21111000000000-4-40000000022222222-1-1-1-1-1-1-1-1000000000000000000000000
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χ594444-24-2-4-4-2-24-2-2-24-2422221-2-211-2-2-21-2-2-22-4-4-1-122222-1-100111122-1-1-1-10000000000000000000−23−23232300003333−3−3−3−3000000000000000000000000
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χ614444-2-2444-2-2-244-2-24-2-2-2-2-2-2-21-2-2-211-2-21-24-2-2-2-211114-2-2-4-41111-2-21111-42222-1-1-1-1002222-1-1-1-10000000000000000000000000000000000000000
χ624444-2-24-4-4-2-2-244-2-24-22222-2-21-2-2-211-2-21-2-42222-1-1-1-1-42244111122-1-1-1-1-42222-1-1-1-100-2-2-2-211110000000000000000000000000000000000000000
χ634444-2-24-4-4-2-2-244-2-24-22222-2-21-2-2-211-2-21-2-42222-1-1-1-1-422-4-4111122-1-1-1-14-2-2-2-21111002222-1-1-1-10000000000000000000000000000000000000000
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χ7144-4-4-24-2002-24-222-42-423−23−23231-2-2-11-22-2-12220003−323−23−23230−33001-11-100−333−3000000000000000000000006−6−66ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23000000000000000000000000
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χ824-44-44-24004-42-4-4-4-24200004-2-24-42-22-422-2000000000000−4i4i-2-22200000000000000000−4i4i2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
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χ884-44-4-2-2400-222-4-42-24223−2323−23-2-21-2221-122-1-200023−23−3−333023−23−4i4i11-1-100−3−33302i3−2i300−i3−i3i3i3002i−2i2i−2i−i−iii0000000000000000000000000000000000000000
χ894-44-4-2-2400-222-4-42-242−2323−2323-2-21-2221-122-1-2000−232333−3−30−23234i−4i11-1-10033−3−302i3−2i300−i3−i3i3i300−2i2i−2i2iii−i−i0000000000000000000000000000000000000000
χ904-44-4-2-2400-222-4-42-242−2323−2323-2-21-2221-122-1-2000−232333−3−30−2323−4i4i11-1-10033−3−30−2i32i300i3i3−i3−i3002i−2i2i−2i−i−iii0000000000000000000000000000000000000000
χ914-4-4444-24-4-4-4-42-24-42444-4-4-2-24222-4-4-2-24224-4224-44-4-2-2-200-222-2-22-22-2200000000000000000000000000000000000000000000000000000000000
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χ934-4-444-24-44-4-42-4442-4-2-4-4444-2-2-4-42224-2-2242-2442-22-2-4-4-400-222-22-22-22-200000000000000000000000000000000000000000000000000000000000
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χ954-4-444-2-24-4-4-422-2422-244-4-4-21-222-122-21-2-12-2222-22-22-2-2-2001-1-111-11-11-10000000000000000000000000000000000000000−3i3i3i−3i000000000000000
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χ1088888-4-4-488-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222-4-4-4222222-42200-1-1-1-122-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1098888-4-4-4-8-8-4-4-4-4-4-4-4-4-44444222222222222444-2-2-2-2-2-24-2-200-1-1-1-1-2-2111100000000000000000000000000000000000000000000000000000000000
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χ11288-8-8-4-4-4004-4-4-444444−434343−43222-222-22-2-2-2-2000−232323−23−2323023−2300-11-1100−333−300000000000000000000000000000000000000000000000000000000000
χ1138-88-88-4-4008-8444-8-4-440000-42-4-44-2-444-2420000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
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χ1158-88-8-4-4-400-444444-4-44−4343−43432222-2-22-2-2-2-2200023−232323−23−23023−2300-1-11100−3−33300000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-48-84444-4-444-4-4-444222-2-2-2-2-2222-24-44-2-22-22-2-42200-111-12-2-11-1100000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4-884444-4-444-444-4-4222-2-2-2-2-2222-2-44-422-22-224-2-200-111-1-221-11-100000000000000000000000000000000000000000000000000000000000

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