Finite Group Databasebeta

← Group #13156668

Character table — Group #13156668

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-111-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-11
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111111-1
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χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-2000000000000000000000000-2-222-2-2-2-222220000000000000000
χ11222222-1222222-1-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
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χ13222222-1222222-1-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ14222222-1222222-1-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000
χ15222222-1-2-22222-1-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111000000003333−3−3−3−33333−3−3−3−3-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−322-2-2-1-1-1-111110000000000000000
χ16222222-1-2-22222-1-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111000000003333−3−3−3−3−3−3−3−33333-1-1-1-1-2-2111100003333−3−3−3−30000−3−3−3−33333-2-2221111-1-1-1-10000000000000000
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χ18222222-1-2-22222-1-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-2111100000000−3−3−3−33333−3−3−3−33333-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−3333322-2-2-1-1-1-111110000000000000000
χ1922222-12222-12-12222-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000222-1-1-1-1-1-10200-1-10
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χ232222-12222-12-12222-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-1-122-1-1-1-120-1-1000
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χ252222-12222-12-12222-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000002-1-122-1-1-1-1-2011000
χ262222-12222-12-12222-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-211-2-2111120-1-1000
χ2722-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2222-22-222-2-2-22-2-222000022-2-20000000022-2-222-2-22-2-222-222-2-200000000000022-2-222-2-222-2-20000000000000000000000000000
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χ3022-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2222-2-22-2-2222-222-2-2-2-2220000-2-222-2-222000000002-2-22-22-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ3122-2-222-12-2-2-222-111-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1000022-2-233−3−3−3−333-1-111-1-111-111-12-2-1-111000033−3−3−3−33322-2-2-1-111-1-111000033−3−333−3−30000000000000000
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χ3522-2-222-1-22-2-222-111-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-11122-2-20000-1-111-1-11133−3−3−3−333-111-1-2211-1-122-2-2-1-111-1-111000033−3−3−3−3330000−3−33333−3−30000000000000000
χ3622-2-222-1-22-2-222-111-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-11122-2-20000-1-111-1-111−3−33333−3−3-111-1-2211-1-122-2-2-1-111-1-1110000−3−33333−3−3000033−3−3−3−3330000000000000000
χ3722-2-222-1-22-2-222-111-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-2-222000011-1-111-1-133−3−3−3−333-111-1-2211-1-1-2-22211-1-111-1-1000033−3−3−3−333000033−3−3−3−3330000000000000000
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χ3922-2-22-122-2-212-12-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-1110000000000000003−333−3−300003−30
χ4022-2-22-122-2-212-12-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-111000000000000000−33−3−3330000−330
χ4122-2-22-122-2-212-12-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-10000-2-22200000000-2-222-2-222-111-1-11-1-11100000000000011-1-111-1-111-1-10000000000000003−333−3−30000−330
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χ4322-2-2-122-221-2-122-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-222-2-2000022-2-222-2-200000000-111-11-111-1-1-1-111-1-111-1-11100000000000000000000000003−3003−33−3003−3000
χ4422-2-2-122-221-2-122-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-222-2-2000022-2-222-2-200000000-111-11-111-1-1-1-111-1-111-1-1110000000000000000000000000−3300−33−3300−33000
χ4522-2-2-122-221-2-122-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-2-2220000-2-222-2-22200000000-111-11-111-1-111-1-111-1-111-1-100000000000000000000000003−3003−33−300−33000
χ4622-2-2-122-221-2-122-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-2-2220000-2-222-2-22200000000-111-11-111-1-111-1-111-1-111-1-10000000000000000000000000−3300−33−33003−3000
χ472-22-22220022-2-2-22-2-2-2000022222-22-2-2-2-2-20000000000002−22−22−22−22−22−22−22−22−22−22−22−222-2-20000002−22−22−22−22−22−22−22−22−22−22−22−22-2002-22-200000000000000000000
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χ492-22-22220022-2-2-22-2-2-2000022222-22-2-2-2-2-2000000000000−22−222−22−2−22−22−22−222−22−22−22−222-2-2000000−22−22−22−22−22−222−22−22−22−22−22−2-2200-22-2200000000000000000000
χ502-22-22220022-2-2-22-2-2-2000022222-22-2-2-2-2-2000000000000−22−22−22−22−22−22−22−22−22−22−22−2222-2-2000000−22−22−22−22−22−22−22−22−22−22−22−222-2002-22-200000000000000000000
χ512-22-222-10022-2-21-11-2-23−33−32-1-12-11-11-211-2003−33−3003−33−32−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-1-111003−33−32−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ232-200-11-113−33−30000000000000000
χ522-22-222-10022-2-21-11-2-23−33−32-1-12-11-11-211-2003−33−3003−33−32−22−2−22−22ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-1-111003−33−32−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-22001-11-1−33−330000000000000000
χ532-22-222-10022-2-21-11-2-23−33−32-1-12-11-11-211-2003−33−3003−33−3−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-1-111003−33−3−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-22001-11-1−33−330000000000000000
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χ552-22-222-10022-2-21-11-2-2−33−332-1-12-11-11-211-200−33−3300−33−332−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-1-11100−33−332−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72-200-11-11−33−330000000000000000
χ562-22-222-10022-2-21-11-2-2−33−332-1-12-11-11-211-200−33−3300−33−332−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-1-11100−33−332−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-22001-11-13−33−30000000000000000
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χ582-22-222-10022-2-21-11-2-2−33−332-1-12-11-11-211-200−33−3300−33−33−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-1-11100−33−33−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ72-200-11-11−33−330000000000000000
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χ1224-4-44-24-2002-42-422-2-24−232323−23-21-22-112-22-12-2003−323−2300−33−2323−222222−220000−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23000000001-11-1003−3−332−2−22ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ230000000000000000000000000000000000000000
χ1238888-4-4-488-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222-4-42222-4-42222000000000000000000000000-1-1-1-122-1-1-1-10000000000000000000000000000000000000000000000000000
χ1248888-4-4-4-8-8-4-4-4-4-4-4-4-4-4444422222222222244-2-2-2-244-2-2-2-2000000000000000000000000-1-1-1-1-2-211110000000000000000000000000000000000000000000000000000
χ12588-8-8-4-4-48-844-4-4-44444-4-444222-2-2-2-2-2222-2-4422-2-24-4-2-222000000000000000000000000-111-12-2-1-1110000000000000000000000000000000000000000000000000000
χ12688-8-8-4-4-4-8844-4-4-4444444-4-4222-2-2-2-2-2222-24-4-2-222-4422-2-2000000000000000000000000-111-1-2211-1-10000000000000000000000000000000000000000000000000000
χ1278-88-8-4-4800-4-444-88-84400002-4-42-44-44-244-200000000000000000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ1288-88-8-4-4-400-4-4444-444443−4343−4322222-22-2-2-2-2-200−2323−232300−2323−2323000000000000000000000000-1-111003−33−30000000000000000000000000000000000000000000000000000
χ1298-88-8-4-4-400-4-4444-4444−4343−434322222-22-2-2-2-2-20023−2323−230023−2323−23000000000000000000000000-1-11100−33−330000000000000000000000000000000000000000000000000000
χ1308-8-88-4-48004444-8-88-4-400002-4-4-24-44-4-24420000000000000000000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1318-8-88-4-4-400444444-4-4-443−43−4343222-2-22-22-2-2-2200−232323−230023−23−2323000000000000000000000000-11-11003−3−330000000000000000000000000000000000000000000000000000
χ1328-8-88-4-4-400444444-4-4-4−434343−43222-2-22-22-2-2-220023−23−232300−232323−23000000000000000000000000-11-1100−333−30000000000000000000000000000000000000000000000000000

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