Finite Group Databasebeta

← Group #13156316

Character table — Group #13156316

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222222222444444444444444444444444668888888888121212121212121212121212121212121212121212121212121212121212121212121224242424242424242436363636363636367272727272108108
order1222333446666666661212121233366666666612121212121212121212121244366612121212121248812121212121212121212121212121212242424242424242424242424242424244121212121212121244882424242441212121244
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2002222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2200-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ11222222-12222-122-122-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-120022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000222-1-1-1-1-1-100000000200-1-100
χ12222222-12222-122-122-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-120022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-211111100000000-2001100
χ13222222-12222-122-122-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-211-2-211111111110000000000000000222-1-1-1-1-1-100000000-2001100
χ14222222-12222-122-122-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-211-2-211111111110000000000000000-2-2-211111100000000200-1-100
χ15222222-1-2-222-122-122-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-222-1-1-1-1111111-20022-1-1-2-211-1-1-1-111110000000000000000000−i3i3−i3−i3i3i300000000000−i3i300
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χ17222222-1-2-222-122-122-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-2-2-1-1-1-1111111200-2-21122-1-11111-1-1-1-10000000000000000000−i3i3−i3−i3i3i300000000000i3−i300
χ18222222-1-2-222-122-122-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-2-2-1-1-1-1111111200-2-21122-1-11111-1-1-1-10000000000000000000i3−i3i3i3−i3−i300000000000−i3i300
χ1922222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000022-1-1-1-10000000
χ2022222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-2-2-1-122-1-122-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000000-2-211110000000
χ2122222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-22211-2-211-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-100000000000-2-211110000000
χ2222222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-2-2-211-2-211-2-2111111111111-2-2-2-2111111110000000000022-1-1-1-10000000
χ2322222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-21122-1-1-1-1-2-21111-200-1-12211-2-2-1-1-1-1111133−3−300003333−3−3−3−3000000000000033−3−30000000
χ2422222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-21122-1-1-1-1-2-21111-200-1-12211-2-2-1-1-1-11111−3−3330000−3−3−3−333330000000000000−3−3330000000
χ2522222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-2-2-1-1221111-1-1-1-133−3−300003333−3−3−3−30000000000000−3−3330000000
χ2622222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-2-2-1-1221111-1-1-1-1−3−3330000−3−3−3−33333000000000000033−3−30000000
χ272222-12222-122222-1-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1220000000-1-10000
χ282222-12222-122222-1-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-21111-2-20000000110000
χ292222-12222-122222-1-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-21111111111112-1-122-1-1-1-1-2-20000000110000
χ302222-12222-122222-1-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-2111111111111-211-2-21111220000000-1-10000
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χ3222-2-2222002-2-22-22-2-2-200002222-22-2-2-22-2-20000000000002-222-2-20000000−222-22-2000022-2-20000−22−22−2−222−2−222−2−22200000000000−22−22−220000000
χ3322-2-2222002-2-22-22-2-2-200002222-22-2-2-22-2-2000000000000-2222-2-200000002−2-22-220000-2-22200002−22−222−2−222−2−222−2−200000000000−22−22−220000000
χ3422-2-2222002-2-22-22-2-2-200002222-22-2-2-22-2-2000000000000-2222-2-20000000−22-22-220000-2-2220000−22−22−2−222−2−222−2−222000000000002−22−22−20000000
χ3522-2-22-120021-2-112-2-2-23−33−3-12-1-1121-21-11-20003−333−3−303−32-2-1-1110033−3−302−2-112-23−300-1-11133−3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ3622-2-22-120021-2-112-2-2-23−33−3-12-1-1121-21-11-20003−333−3−303−32-2-1-1110033−3−30−22-112-23−300-1-11133−3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ3722-2-22-120021-2-112-2-2-23−33−3-12-1-1121-21-11-20003−333−3−303−3-22-1-1110033−3−302−21-1-22−330011-1-1−3−333ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ3822-2-22-120021-2-112-2-2-23−33−3-12-1-1121-21-11-20003−333−3−303−3-22-1-1110033−3−30−221-1-22−330011-1-1−3−333−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ3922-2-22-120021-2-112-2-2-2−33−33-12-1-1121-21-11-2000−33−3−3330−332-2-1-11100−3−33302−2-112-2−3300-1-111−3−333ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ4022-2-22-120021-2-112-2-2-2−33−33-12-1-1121-21-11-2000−33−3−3330−332-2-1-11100−3−3330−22-112-2−3300-1-111−3−333−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ4122-2-22-120021-2-112-2-2-2−33−33-12-1-1121-21-11-2000−33−3−3330−33-22-1-11100−3−33302−21-1-223−30011-1-133−3−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
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χ442-22-22222-2-222-2-2-2-22-222-2-2222-2-2-2222-2-2-22-22222-22-2-2-2-2002-2-222-22-22-200000000000000000000000000000000000000000000-220000000-220000
χ452-22-2222-22-222-2-2-2-22-2-2-222222-2-2-2222-2-2-2-22-2-2-2-22-22222002-2-22-22-22-220000000000000000000000000000000000000000000000000000000002i−2i
χ462-22-2222-22-222-2-2-2-22-2-2-222222-2-2-2222-2-2-2-22-2-2-2-22-22222002-2-22-22-22-22000000000000000000000000000000000000000000000000000000000−2i2i
χ472-22-2-1222-2122-2-2-21-1-222-2-2-1-12111-1-12-2-212-2-1-1-12-22-211100-111-1-11-11-11000000000000000000000003−33−33−33−33−33−303−3003−33−32-20000000-110000
χ482-22-2-1222-2122-2-2-21-1-222-2-2-1-12111-1-12-2-212-2-1-1-12-22-211100-111-1-11-11-11000000000000000000000003−33−33−33−33−33−30−3300−33−33-2200000001-10000
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χ554444-244-4-4-244444-2-24-4-4-4-4-2-24-2-2-2-2-2444-2-4-4222-4-4-4-422200-2-2-2-222222200000000000000000000000000000000000000000000000000000000000
χ564444-24-244-24-244-2-2-2-24444-21-2-2-21-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2001111111111000000000000000000000000000000000004-2-2-2-21111000000000000000
χ574444-24-244-24-244-2-2-2-24444-21-2-2-21-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-200111111111100000000000000000000000000000000000-42222-1-1-1-1000000000000000
χ584444-24-2-4-4-24-244-2-2-2-2-4-4-4-4-21-2-2-21-21-2-2-21222222222222001111-1-1-1-1-1-100000000000000000000000000000000000000−2i32i3i3i3−i3−i3000000000000000
χ594444-24-2-4-4-24-244-2-2-2-2-4-4-4-4-21-2-2-21-21-2-2-21222222222222001111-1-1-1-1-1-1000000000000000000000000000000000000002i3−2i3−i3−i3i3i3000000000000000
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χ1024-4-44-244002-4-4-44-4-2240000-2-242-2222-4-44-200000000000000-22-22000000000000000000000000000006−6−666−6−666−6−66000000000000000000000000
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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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χ1158-8-88-48-4004-84-884-44-40000-42-44-4-24-244-42000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.