Finite Group Databasebeta

← Group #13155973

Character table — Group #13155973

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222222222444444444444444444444444668888888888121212121212121212121212121212121212121212121212121212121212121212121224242424242424242436363636363636367272727272108108
order1222333446666666661212121233366666666612121212121212121212121244366612121212121248812121212121212121212121212121212242424242424242424242424242424242666666662288242424242666644
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
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
χ11222222-1222222-122-1-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-120022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000222-1-1-1-1-1-1000000002-1-10000
χ12222222-1222222-122-1-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-120022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-211111100000000-2110000
χ13222222-1222222-122-1-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-211-2-211111111110000000000000000222-1-1-1-1-1-100000000-2110000
χ14222222-1222222-122-1-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-211-2-211111111110000000000000000-2-2-2111111000000002-1-10000
χ15222222-1-2-22222-122-1-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-20022-1-1-2-211-1-1-1-111110000000000000000000−i3i3−i3−i3i3i3000000000−i3i30000
χ16222222-1-2-22222-122-1-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-20022-1-1-2-211-1-1-1-111110000000000000000000i3−i3i3i3−i3−i3000000000i3−i30000
χ17222222-1-2-22222-122-1-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111200-2-21122-1-11111-1-1-1-10000000000000000000−i3i3−i3−i3i3i3000000000i3−i30000
χ18222222-1-2-22222-122-1-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111200-2-21122-1-11111-1-1-1-10000000000000000000i3−i3i3i3−i3−i3000000000−i3i30000
χ1922222-1222-1-12-1222222222-12-1-1-1-1-1-12-122-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-122000000000-1-100
χ2022222-1222-1-12-1222222222-12-1-1-1-1-1-12-122-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-21111-2-20000000001100
χ2122222-1222-1-12-1222222222-12-1-1-1-1-1-12-122-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-21111111111112-1-122-1-1-1-1-2-20000000001100
χ2222222-1222-1-12-1222222222-12-1-1-1-1-1-12-122-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-2111111111111-211-2-2111122000000000-1-100
χ232222-1222222-122-1-122-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000022-1-1-1-10000000
χ242222-1222222-122-1-122-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-2-2-1-122-1-122-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000000-2-211110000000
χ252222-1222222-122-1-122-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-22211-2-211-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-100000000000-2-211110000000
χ262222-1222222-122-1-122-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-2-2-211-2-211-2-2111111111111-2-2-2-2111111110000000000022-1-1-1-10000000
χ272222-122-2-222-122-1-1221111-1-12-1-122-1-12-1-1-2-2-2111111-21122-1-1-1-1-2-21111-200-1-12211-2-2-1-1-1-1111133−3−300003333−3−3−3−3000000000000033−3−30000000
χ282222-122-2-222-122-1-1221111-1-12-1-122-1-12-1-1-2-2-2111111-21122-1-1-1-1-2-21111-200-1-12211-2-2-1-1-1-11111−3−3330000−3−3−3−333330000000000000−3−3330000000
χ292222-122-2-222-122-1-1221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-2-2-1-1221111-1-1-1-133−3−300003333−3−3−3−30000000000000−3−3330000000
χ302222-122-2-222-122-1-1221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-2-2-1-1221111-1-1-1-1−3−3330000−3−3−3−33333000000000000033−3−30000000
χ3122-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2222-2-222-22222-2-2-2-2-2002-2-222-222-2-20000000000000000000000000000000000000000000000000000000002i−2i
χ3222-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2222-2-222-22222-2-2-2-2-2002-2-222-222-2-2000000000000000000000000000000000000000000000000000000000−2i2i
χ3322-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2222-2-2-2-22-2-2-2-222222002-2-22-22-2-222000000000000000000000000000000000000000000002-20000000002-200
χ3422-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2222-2-2-2-22-2-2-2-222222002-2-22-22-2-22200000000000000000000000000000000000000000000-22000000000-2200
χ3522-2-22-12-22112-12-2-2-2-2-2-222-12-11111-12-1-2-21-2211-2-222-1-1-100-111-11-111-1-100000000000000000000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30−i3i300−i3i3−i3i32-2000000000-1100
χ3622-2-22-12-22112-12-2-2-2-2-2-222-12-11111-12-1-2-21-2211-2-222-1-1-100-111-11-111-1-100000000000000000000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30i3−i300i3−i3i3−i3-220000000001-100
χ3722-2-22-12-22112-12-2-2-2-2-2-222-12-11111-12-1-2-21-2211-2-222-1-1-100-111-11-111-1-100000000000000000000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30−i3i300−i3i3−i3i3-220000000001-100
χ3822-2-22-12-22112-12-2-2-2-2-2-222-12-11111-12-1-2-21-2211-2-222-1-1-100-111-11-111-1-100000000000000000000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30i3−i300i3−i3i3−i32-2000000000-1100
χ392-2-22222002-2-2-2-22-22-200002222-22-2-2-2-22-20000000000002-222-2-200000002−22-22-2000022-2-200002−22−22−22−22−22−22−22−2000000000002−22−22−20000000
χ402-2-22222002-2-2-2-22-22-200002222-22-2-2-2-22-20000000000002-222-2-20000000−222-22-2000022-2-20000−22−22−22−22−22−22−22−2200000000000−22−22−220000000
χ412-2-22222002-2-2-2-22-22-200002222-22-2-2-2-22-2000000000000-2222-2-200000002−2-22-220000-2-22200002−22−22−22−22−22−22−22−200000000000−22−22−220000000
χ422-2-22222002-2-2-2-22-22-200002222-22-2-2-2-22-2000000000000-2222-2-20000000−22-22-220000-2-2220000−22−22−22−22−22−22−22−22000000000002−22−22−20000000
χ432-2-22-122002-21-2-2-112-23−33−3-1-12-112-211-2-110003−33−33−303−32-2-1-111003−33−302−2-112-23−300-1-11133−3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ442-2-22-122002-21-2-2-112-23−33−3-1-12-112-211-2-110003−33−33−303−32-2-1-111003−33−30−22-112-23−300-1-11133−3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ452-2-22-122002-21-2-2-112-23−33−3-1-12-112-211-2-110003−33−33−303−3-22-1-111003−33−302−21-1-22−330011-1-1−3−333ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ462-2-22-122002-21-2-2-112-23−33−3-1-12-112-211-2-110003−33−33−303−3-22-1-111003−33−30−221-1-22−330011-1-1−3−333−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ472-2-22-122002-21-2-2-112-2−33−33-1-12-112-211-2-11000−33−33−330−332-2-1-11100−33−3302−2-112-2−3300-1-111−3−333ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ482-2-22-122002-21-2-2-112-2−33−33-1-12-112-211-2-11000−33−33−330−332-2-1-11100−33−330−22-112-2−3300-1-111−3−333−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ492-2-22-122002-21-2-2-112-2−33−33-1-12-112-211-2-11000−33−33−330−33-22-1-11100−33−3302−21-1-223−30011-1-133−3−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ502-2-22-122002-21-2-2-112-2−33−33-1-12-112-211-2-11000−33−33−330−33-22-1-11100−33−330−221-1-223−30011-1-133−3−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ5144444-24-4-4-2-24-244444-4-4-4-4-24-2-2-2-2-2-24-2442-4-422-4-4-4-422200-2-2-2-222222200000000000000000000000000000000000000000000000000000000000
χ5244444-2-244-2-24-2-244-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2001111111111000000000000000000000000000000000004-2-2-2-21111000000000000000
χ5344444-2-244-2-24-2-244-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-200111111111100000000000000000000000000000000000-42222-1-1-1-1000000000000000
χ5444444-2-2-4-4-2-24-2-244-2-2-4-4-4-4-2-21-2-211-2-21-2-2222222222222001111-1-1-1-1-1-100000000000000000000000000000000000000−2i32i3i3i3−i3−i3000000000000000
χ5544444-2-2-4-4-2-24-2-244-2-2-4-4-4-4-2-21-2-211-2-21-2-2222222222222001111-1-1-1-1-1-1000000000000000000000000000000000000002i3−2i3−i3−i3i3i3000000000000000
χ564444-24-24444-24-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2-21-2114-2-2-2-211114-2-2441111-2-21111400-2-2-2-2-2-2-2-2111111110000000000000000000000000000000000000000
χ574444-24-24444-24-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2-21-2114-2-2-2-211114-2-2-4-41111-2-21111-40022222222-1-1-1-1-1-1-1-10000000000000000000000000000000000000000
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χ614444-2-2444-2-2-2-24-2-244-2-2-2-21-2-211-2-21-2-2-2-2-24411-2-2-2-2-211001111-2-211110-4-4000000000000000022222222-1-1-1-1-1-1-1-1000000000000000000000000
χ624444-2-24-4-4-2-2-2-24-2-24422221-2-211-2-21-2-2-2-22-4-4-1-122222-1-100111122-1-1-1-100000000000000000002323−23−230000−3−3−3−33333000000000000000000000000
χ634444-2-24-4-4-2-2-2-24-2-24422221-2-211-2-21-2-2-2-22-4-4-1-122222-1-100111122-1-1-1-10000000000000000000−23−23232300003333−3−3−3−3000000000000000000000000
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χ6544-4-444-2-44-4-444-2-4-422-4-4444-2-2-4-4224-2-222-42-2-4-422-2-244400-222-22-222-2-200000000000000000000000000000000000000000000000000000000000
χ6644-4-44-244-4224-24-4-4-4-444-4-4-24-22222-24-2-4-4-24-4-2-244-4-422200-222-2-22-2-22200000000000000000000000000000000000000000000000000000000000
χ6744-4-44-2-24-4224-2-2-4-42244-4-4-2-2122-1-1-2-2122-2-22-2-2-2-222222001-1-111-111-1-100000000000000000000000000000000000000003-3-33000000000000000
χ6844-4-44-2-24-4224-2-2-4-42244-4-4-2-2122-1-1-2-2122-2-22-2-2-2-222222001-1-111-111-1-10000000000000000000000000000000000000000-333-3000000000000000
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χ7144-4-4-2444-4-4-4-24422-4-4-2-222-2-2422-4-4-2-242244-4-2-2-2-222-42200-222-24-4-2-22200000000000000000000000000000000000000000000000000000000000
χ7244-4-4-244-44-4-4-24422-4-422-2-2-2-2422-4-4-2-2422-4-442222-2-24-2-200-222-2-4422-2-200000000000000000000000000000000000000000000000000000000000
χ7344-4-4-24-24-4-4-4-24-22222-2-222-21-22222-21-2-1-14-22-2-211-1-1-422001-1-11-2211-1-1000000000003i−3i3i−3i3i−3i3i−3i0000000000000000000000000000000000000000
χ7444-4-4-24-24-4-4-4-24-22222-2-222-21-22222-21-2-1-14-22-2-211-1-1-422001-1-11-2211-1-100000000000−3i3i−3i3i−3i3i−3i3i0000000000000000000000000000000000000000
χ7544-4-4-24-2-44-4-4-24-2222222-2-2-21-22222-21-2-1-1-42-222-1-1114-2-2001-1-112-2-1-111000000000003i−3i3i−3i−3i3i−3i3i0000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.