Finite Group Databasebeta

← Group #13156341

Character table — Group #13156341

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222222222444444444444444444444444668888888888121212121212121212121212121212121212121212121212121212121212121212121224242424242424242436363636363636367272727272108108
order12223334466666666612121212333666666666121212121212121212121212443666121212121212488121212121212121212121212121212122424242424242424242424242424242441212121212121212228824242424466121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-20022-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2200-2-222-2-222-2-2-2-222220000000000000000000000000000000000000000
χ11222222-122-122-122-12222222-1-1-1-1-12-1-122-122-12222-1-1-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1220000000-1-10000
χ12222222-122-122-122-12222222-1-1-1-1-12-1-122-122-12222-1-1-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-21111-2-20000000110000
χ13222222-122-122-122-12222222-1-1-1-1-12-1-122-122-12222-1-1-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-21111111111112-1-122-1-1-1-1-2-20000000110000
χ14222222-122-122-122-12222222-1-1-1-1-12-1-122-122-12222-1-1-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-2111111111111-211-2-21111220000000-1-10000
χ1522222-122222-12222-1-12222-12-122-1-12-1-1-1-1-1-12-1-1-1-12222222-1-1-1-1-1-1-1-1-1-12002222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000222-1-1-1-1-1-100000000200-1-100
χ1622222-122222-12222-1-12222-12-122-1-12-1-1-1-1-1-12-1-1-1-12222222-1-1-1-1-1-1-1-1-1-12002222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-211111100000000-2001100
χ1722222-122222-12222-1-12222-12-122-1-12-1-1-1-1-1-12-1-1-1-122222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-2-2-21111111111110000000000000000222-1-1-1-1-1-100000000-2001100
χ1822222-122222-12222-1-12222-12-122-1-12-1-1-1-1-1-12-1-1-1-122222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-2-2-21111111111110000000000000000-2-2-211111100000000200-1-100
χ1922222-12-2-222-12222-1-1-2-2-2-2-12-122-1-12-1-1-1-111-21111-2-2-2-2-222-1-1-1-1111111-20022-2-2-1-111-1-1-1-111110000000000000000000−i3i3−i3−i3i3i300000000000−i3i300
χ2022222-12-2-222-12222-1-1-2-2-2-2-12-122-1-12-1-1-1-111-21111-2-2-2-2-222-1-1-1-1111111-20022-2-2-1-111-1-1-1-111110000000000000000000i3−i3i3i3−i3−i300000000000i3−i300
χ2122222-12-2-222-12222-1-1-2-2-2-2-12-122-1-12-1-1-1-111-21111-2-2-2-2-2-2-2-1-1-1-1111111200-2-22211-1-11111-1-1-1-10000000000000000000−i3i3−i3−i3i3i300000000000i3−i300
χ2222222-12-2-222-12222-1-1-2-2-2-2-12-122-1-12-1-1-1-111-21111-2-2-2-2-2-2-2-1-1-1-1111111200-2-22211-1-11111-1-1-1-10000000000000000000i3−i3i3i3−i3−i300000000000−i3i300
χ232222-122222-122-1-1222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000022-1-1-1-10000000
χ242222-122222-122-1-1222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-2-2-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000000-2-211110000000
χ252222-122222-122-1-1222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-2221111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-100000000000-2-211110000000
χ262222-122222-122-1-1222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-2-2-21111-2-2-2-2111111111111-2-2-2-2111111110000000000022-1-1-1-10000000
χ272222-122-2-22-122-1-12221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-1-1-1-1-2-21111-200-1-11122-2-2-1-1-1-1111133−3−300003333−3−3−3−3000000000000033−3−30000000
χ282222-122-2-22-122-1-12221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-1-1-1-1-2-21111-200-1-11122-2-2-1-1-1-11111−3−3330000−3−3−3−333330000000000000−3−3330000000
χ292222-122-2-22-122-1-12221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-1-1-2-2221111-1-1-1-133−3−300003333−3−3−3−30000000000000−3−3330000000
χ302222-122-2-22-122-1-12221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-1-1-2-2221111-1-1-1-1−3−3330000−3−3−3−33333000000000000033−3−30000000
χ3122-2-22222-2-2222-2-2-2-2-222-2-2222-2-2-2222-2-2-22-2222-2-222-2-2-2002-2-222-222-2-2000000000000000000000000000000000000000000002-200000002-20000
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χ3322-2-2222-22-2222-2-2-2-2-2-2-222222-2-2-2222-2-2-2-22-2-2-222-2-2222002-2-22-22-2-2220000000000000000000000000000000000000000000000000000000002i−2i
χ3422-2-2222-22-2222-2-2-2-2-2-2-222222-2-2-2222-2-2-2-22-2-2-222-2-2222002-2-22-22-2-222000000000000000000000000000000000000000000000000000000000−2i2i
χ3522-2-222-12-2122-1-2-21-2-222-2-22-1-11112-1-1-2-212-2-122-2-2-1-111100-111-1-11-1-1110000000000000000000000033−3−333−3−333−3−303−3003−33−32-20000000-110000
χ3622-2-222-12-2122-1-2-21-2-222-2-22-1-11112-1-1-2-212-2-122-2-2-1-111100-111-1-11-1-1110000000000000000000000033−3−333−3−333−3−30−3300−33−33-2200000001-10000
χ3722-2-222-12-2122-1-2-21-2-222-2-22-1-11112-1-1-2-212-2-122-2-2-1-111100-111-1-11-1-11100000000000000000000000−3−333−3−333−3−33303−3003−33−3-2200000001-10000
χ3822-2-222-12-2122-1-2-21-2-222-2-22-1-11112-1-1-2-212-2-122-2-2-1-111100-111-1-11-1-11100000000000000000000000−3−333−3−333−3−3330−3300−33−332-20000000-110000
χ392-22-2222002-2-2-22-2-2-2200002222-22-2-2-22-2-20000000000002i−2i22-2-20000000−i2i22i−2i002i−2i002i2i−2i−2i0000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000002−22−22−20000000
χ402-22-2222002-2-2-22-2-2-2200002222-22-2-2-22-2-20000000000002i−2i22-2-20000000i2−i22i−2i002i−2i002i2i−2i−2i0000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000−22−22−220000000
χ412-22-2222002-2-2-22-2-2-2200002222-22-2-2-22-2-2000000000000−2i2i22-2-20000000−i2i2−2i2i00−2i2i00−2i−2i2i2i0000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000−22−22−220000000
χ422-22-2222002-2-2-22-2-2-2200002222-22-2-2-22-2-2000000000000−2i2i22-2-20000000i2−i2−2i2i00−2i2i00−2i−2i2i2i0000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000002−22−22−20000000
χ432-22-2-1220021-2-2-11-2-223−33−3-1-12-11211-2-11-20003−33−33−303−32i−2i-1-111003−33−30−i2i2−ii−i3i32i−2i00−i−iii−i3−i3i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ442-22-2-1220021-2-2-11-2-223−33−3-1-12-11211-2-11-20003−33−33−303−32i−2i-1-111003−33−30i2−i2−ii−i3i32i−2i00−i−iii−i3−i3i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ452-22-2-1220021-2-2-11-2-223−33−3-1-12-11211-2-11-20003−33−33−303−3−2i2i-1-111003−33−30−i2i2i−ii3−i3−2i2i00ii−i−ii3i3−i3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ462-22-2-1220021-2-2-11-2-223−33−3-1-12-11211-2-11-20003−33−33−303−3−2i2i-1-111003−33−30i2−i2i−ii3−i3−2i2i00ii−i−ii3i3−i3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ472-22-2-1220021-2-2-11-2-22−33−33-1-12-11211-2-11-2000−33−33−330−332i−2i-1-11100−33−330−i2i2−iii3−i32i−2i00−i−iiii3i3−i3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ482-22-2-1220021-2-2-11-2-22−33−33-1-12-11211-2-11-2000−33−33−330−332i−2i-1-11100−33−330i2−i2−iii3−i32i−2i00−i−iiii3i3−i3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ492-22-2-1220021-2-2-11-2-22−33−33-1-12-11211-2-11-2000−33−33−330−33−2i2i-1-11100−33−330−i2i2i−i−i3i3−2i2i00ii−i−i−i3−i3i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ502-22-2-1220021-2-2-11-2-22−33−33-1-12-11211-2-11-2000−33−33−330−33−2i2i-1-11100−33−330i2−i2i−i−i3i3−2i2i00ii−i−i−i3−i3i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ51444444-2-4-4-244-244-244-4-4-4-44-2-2-2-2-24-2-244-2-4-42-4-4-4-42222200-2-2-2-222222200000000000000000000000000000000000000000000000000000000000
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χ5444444-2-2-4-4-24-2-244-2-2-2-4-4-4-4-2-21-2-21-2-21-2-21222222222222001111-1-1-1-1-1-100000000000000000000000000000000000000−2i32i3i3i3−i3−i3000000000000000
χ5544444-2-2-4-4-24-2-244-2-2-2-4-4-4-4-2-21-2-21-2-21-2-21222222222222001111-1-1-1-1-1-1000000000000000000000000000000000000002i3−2i3−i3−i3i3i3000000000000000
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χ7144-4-4-2444-4-4-24422-4-4-4-2-222-2-2422-4-2-2422-44-44-2-222-2-2-42200-222-24-4-2-22200000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.