Finite Group Databasebeta

← Group #13156682

Character table — Group #13156682

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212242424242424242424363636363636727272727272216
order1222333446666666661212121233366666666612121212121212121212121236661212121212128888242424242424242424242424242424242424242424242424242424242424242441212121212121212441212121244121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000000002-222-2-20000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000000-22-2-2220000000
χ11222222-122222-12-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10000000
χ12222222-122222-12-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000-2-211110000000
χ13222222-122222-12-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1000000000-2-211110000000
χ14222222-122222-12-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111100000000022-1-1-1-10000000
χ15222222-1-2-2222-12-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−30000000002-2-1-1110000000
χ16222222-1-2-2222-12-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333000000000-2211-1-10000000
χ17222222-1-2-2222-12-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3000000000-2211-1-10000000
χ18222222-1-2-2222-12-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−333330000000002-2-1-1110000000
χ1922222-122222-12-122-122222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-122-1-1-1-100000020-1-1000
χ2022222-122222-12-122-122222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-211-2-21111000000-2011000
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χ232222-12222-1-1222222-12222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000200-1-10
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χ252222-12222-1-1222222-12222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-2000000000000111111111111222-1-1-1-1-1-10000000-200110
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χ2722-2-22222-2-2222-2-2-2-2-222-2-2222-2-2-2-2-2222-22-222-2-2-22-2-2222-2-222-222-2-22-2002-22-2000022-2-222-2-222-2-20000000000000000000000000000000000
χ2822-2-22222-2-2222-2-2-2-2-222-2-2222-2-2-2-2-2222-22-222-2-2-22-2-2222-2-222-222-2-2-2200-22-220000-2-222-2-222-2-2220000000000000000000000000000000000
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χ3022-2-2222-22-2222-2-2-2-2-2-2-222222-2-2-2-2-2222-2-22-2-2222-222-2-22-2-22-22-2-22200-220000-22-22000000000000-2-222-2-222-2-2220000000000000000000000
χ3122-2-222-12-2-222-1-211-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1-111-12-2-1-1112-200-11-113−3−3322-2-2-1-111-1-111000033−3−3−3−333000000000003−33−30000000
χ3222-2-222-12-2-222-1-211-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1-111-12-2-1-1112-200-11-11−333−322-2-2-1-111-1-1110000−3−33333−3−300000000000−33−330000000
χ3322-2-222-12-2-222-1-211-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1-111-12-2-1-111-22001-11-13−3−33-2-22211-1-111-1-1000033−3−3−3−33300000000000−33−330000000
χ3422-2-222-12-2-222-1-211-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1-111-12-2-1-111-22001-11-1−333−3-2-22211-1-111-1-10000−3−33333−3−3000000000003−33−30000000
χ3522-2-222-1-22-222-1-211-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-111-1-2211-1-1002-23−3−33-11-11000033−3−3−3−33322-2-2-1-111-1-11100000000000−333−30000000
χ3622-2-222-1-22-222-1-211-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-111-1-2211-1-1002-2−333−3-11-110000−3−33333−3−322-2-2-1-111-1-111000000000003−3−330000000
χ3722-2-222-1-22-222-1-211-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-111-1-2211-1-100-223−3−331-11-1000033−3−3−3−333-2-22211-1-111-1-1000000000003−3−330000000
χ3822-2-222-1-22-222-1-211-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-111-1-2211-1-100-22−333−31-11-10000−3−33333−3−3-2-22211-1-111-1-100000000000−333−30000000
χ3922-2-22-122-2-22-121-2-21-222-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1-111-1-11-1-1112-2002-22-20000-1-111-1-111-1-11100000000000003−30033−3−3000000003−3000
χ4022-2-22-122-2-22-121-2-21-222-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1-111-1-11-1-1112-2002-22-20000-1-111-1-111-1-1110000000000000−3300−3−33300000000−33000
χ4122-2-22-122-2-22-121-2-21-222-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1-111-1-11-1-111-2200-22-22000011-1-111-1-111-1-100000000000003−30033−3−300000000−33000
χ4222-2-22-122-2-22-121-2-21-222-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1-111-1-11-1-111-2200-22-22000011-1-111-1-111-1-10000000000000−3300−3−333000000003−3000
χ4322-2-2-122-221-122-2-2-2-21-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-111-1-1002-200002-22-2000000000000-1-111-1-111-1-1110003−33−33−300000000003−30
χ4422-2-2-122-221-122-2-2-2-21-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-111-1-1002-200002-22-2000000000000-1-111-1-111-1-111000−33−33−330000000000−330
χ4522-2-2-122-221-122-2-2-2-21-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-111-1-100-220000-22-2200000000000011-1-111-1-111-1-10003−33−33−30000000000−330
χ4622-2-2-122-221-122-2-2-2-21-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-111-1-100-220000-22-2200000000000011-1-111-1-111-1-1000−33−33−3300000000003−30
χ4744444-24-4-444-24-244-24-4-4-4-4-24-2-244-2-2-24-2-2-42-4-422-42-4-422-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
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χ534444-24-244-2-24-24-2-24-2-2-2-2-2-21-2-211-2-2-21-2-2-2411-2-2-2411-2-21111-2-2111100440000-2-2-2-2000000000000-2-2-2-2111111110000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.