Finite Group Databasebeta

← Group #13156652

Character table — Group #13156652

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
order1222333446666666661212121233366666666612121212121212121212121288888888242424242424242424242424242424243666121212121212242424242424242424242424242424242424242424242424444412121212121212124121212121212121244121212124
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-200000000000000000000000022-2-22222-2-2-2-20000000000000000
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
χ11222222-12222-122-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ12222222-12222-122-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111110000000000000000
χ13222222-12222-122-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ14222222-12222-122-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000
χ15222222-1-2-222-122-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111000000003333−3−3−3−33333−3−3−3−3-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−322-2-2-1-1-1-111110000000000000000
χ16222222-1-2-222-122-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111000000003333−3−3−3−3−3−3−3−33333-1-1-1-1-2-2111100003333−3−3−3−30000−3−3−3−33333-2-2221111-1-1-1-10000000000000000
χ17222222-1-2-222-122-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-2111100000000−3−3−3−333333333−3−3−3−3-1-1-1-1-2-211110000−3−3−3−3333300003333−3−3−3−3-2-2221111-1-1-1-10000000000000000
χ18222222-1-2-222-122-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-2111100000000−3−3−3−33333−3−3−3−33333-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−3333322-2-2-1-1-1-111110000000000000000
χ1922222-12222-122-1222-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000222-1-1-1-1-1-10200-1-10
χ2022222-12222-122-1222-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-21111110-200110
χ2122222-12222-122-1222-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000222-1-1-1-1-1-10-200110
χ2222222-12222-122-1222-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000-2-2-21111110200-1-10
χ232222-12222-122-1222-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-1-122-1-1-1-120-1-1000
χ242222-12222-122-1222-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-211-2-21111-2011000
χ252222-12222-122-1222-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000002-1-122-1-1-1-1-2011000
χ262222-12222-122-1222-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-211-2-2111120-1-1000
χ2722-2-22222-2222-2-2-2-2-2-222-2-2222-2-2-2-2-2222-22-222-2-2-22-2-222000022-2-20000000022-2-222-2-22-2-222-222-2-200000000000022-2-222-2-222-2-20000000000000000000000000000
χ2822-2-22222-2222-2-2-2-2-2-222-2-2222-2-2-2-2-2222-22-222-2-2-22-2-2220000-2-22200000000-2-222-2-2222-2-222-222-2-2000000000000-2-222-2-222-2-2220000000000000000000000000000
χ2922-2-2222-22222-2-2-2-2-2-2-2-222222-2-2-2-2-2222-2-22-2-2222-222-2-222-2-2000022-2-222-2-2000000002-2-22-22-2-22222-2-222-2-222-2-20000000000000000000000000000000000000000
χ3022-2-2222-22222-2-2-2-2-2-2-2-222222-2-2-2-2-2222-2-22-2-2222-222-2-2-2-2220000-2-222-2-222000000002-2-22-22-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ3122-2-222-12-222-1-2-211-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1000022-2-233−3−3−3−333-1-111-1-111-111-12-2-1-111000033−3−3−3−33322-2-2-1-111-1-111000033−3−333−3−30000000000000000
χ3222-2-222-12-222-1-2-211-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1000022-2-2−3−33333−3−3-1-111-1-111-111-12-2-1-1110000−3−33333−3−322-2-2-1-111-1-1110000−3−333−3−3330000000000000000
χ3322-2-222-12-222-1-2-211-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-10000-2-22233−3−3−3−33311-1-111-1-1-111-12-2-1-111000033−3−3−3−333-2-22211-1-111-1-10000−3−333−3−3330000000000000000
χ3422-2-222-12-222-1-2-211-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-10000-2-222−3−33333−3−311-1-111-1-1-111-12-2-1-1110000−3−33333−3−3-2-22211-1-111-1-1000033−3−333−3−30000000000000000
χ3522-2-222-1-2222-1-2-211-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-11122-2-20000-1-111-1-11133−3−3−3−333-111-1-2211-1-122-2-2-1-111-1-111000033−3−3−3−3330000−3−33333−3−30000000000000000
χ3622-2-222-1-2222-1-2-211-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-11122-2-20000-1-111-1-111−3−33333−3−3-111-1-2211-1-122-2-2-1-111-1-1110000−3−33333−3−3000033−3−3−3−3330000000000000000
χ3722-2-222-1-2222-1-2-211-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-2-222000011-1-111-1-133−3−3−3−333-111-1-2211-1-1-2-22211-1-111-1-1000033−3−3−3−333000033−3−3−3−3330000000000000000
χ3822-2-222-1-2222-1-2-211-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-2-222000011-1-111-1-1−3−33333−3−3-111-1-2211-1-1-2-22211-1-111-1-10000−3−33333−3−30000−3−33333−3−30000000000000000
χ3922-2-22-122-22-12-21-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-1110000000000000003−333−3−300003−30
χ4022-2-22-122-22-12-21-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-111000000000000000−33−3−3330000−330
χ4122-2-22-122-22-12-21-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-10000-2-22200000000-2-222-2-222-111-1-11-1-11100000000000011-1-111-1-111-1-10000000000000003−333−3−30000−330
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χ4322-2-2-122-22-1221-2-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-222-2-2000022-2-222-2-200000000-111-11-111-1-1-1-111-1-111-1-11100000000000000000000000003−3003−33−3003−3000
χ4422-2-2-122-22-1221-2-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-222-2-2000022-2-222-2-200000000-111-11-111-1-1-1-111-1-111-1-1110000000000000000000000000−3300−33−3300−33000
χ4522-2-2-122-22-1221-2-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-2-2220000-2-222-2-22200000000-111-11-111-1-111-1-111-1-111-1-100000000000000000000000003−3003−33−300−33000
χ4622-2-2-122-22-1221-2-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-2-2220000-2-222-2-22200000000-111-11-111-1-111-1-111-1-111-1-10000000000000000000000000−3300−33−33003−3000
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χ512-22-222-100-2-21-2-2-11223−33−32-1-12-11-11-211-2003−33−3003−33−3−i2i2−i2i2−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-1-111003−33−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232-200-11-113−33−30000000000000000
χ522-22-222-100-2-21-2-2-11223−33−32-1-12-11-11-211-2003−33−3003−33−3−i2i2−i2i2i2−i2i2−i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-1-111003−33−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-22001-11-1−33−330000000000000000
χ532-22-222-100-2-21-2-2-11223−33−32-1-12-11-11-211-2003−33−3003−33−3i2−i2i2−i2−i2i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-1-111003−33−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-22001-11-1−33−330000000000000000
χ542-22-222-100-2-21-2-2-11223−33−32-1-12-11-11-211-2003−33−3003−33−3i2−i2i2−i2i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-1-111003−33−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232-200-11-113−33−30000000000000000
χ552-22-222-100-2-21-2-2-1122−33−332-1-12-11-11-211-200−33−3300−33−33−i2i2−i2i2−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-1-11100−33−33−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ72-200-11-11−33−330000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.