Finite Group Databasebeta

← Group #13156681

Character table — Group #13156681

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
χ11222222-1222222-1-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10000000
χ12222222-1222222-1-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000-2-211110000000
χ13222222-1222222-1-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1000000000-2-211110000000
χ14222222-1222222-1-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111100000000022-1-1-1-10000000
χ15222222-1-2-22222-1-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−30000000002-2-1-1110000000
χ16222222-1-2-22222-1-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333000000000-2211-1-10000000
χ17222222-1-2-22222-1-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3000000000-2211-1-10000000
χ18222222-1-2-22222-1-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−333330000000002-2-1-1110000000
χ1922222-12222-12-12222-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000200-1-10
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χ232222-12222-12-12222-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-122-1-1-1-100000020-1-1000
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χ3022-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2222-2-22-2-2222-222-2-22-2-22-22-2-222-2200-22-220000-2-222-2-222-2-2220000000000000000000000000000000000
χ3122-2-222-12-2-2-222-111-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1-111-12-2-1-111002-23−3−33-11-11000033−3−3−3−33322-2-2-1-111-1-111000000000003−33−30000000
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χ3322-2-222-12-2-2-222-111-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1-111-12-2-1-11100-223−3−331-11-1000033−3−3−3−333-2-22211-1-111-1-100000000000−33−330000000
χ3422-2-222-12-2-2-222-111-2-2-1-1112-1-1-211112-1-1-22-2-1-111-2211-1-1-111-12-2-1-11100-22−333−31-11-10000−3−33333−3−3-2-22211-1-111-1-1000000000003−33−30000000
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χ3622-2-222-1-22-2-222-111-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-111-1-2211-1-12-200-11-11−333−322-2-2-1-111-1-1110000−3−33333−3−3000000000003−3−330000000
χ3722-2-222-1-22-2-222-111-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-111-1-2211-1-1-22001-11-13−3−33-2-22211-1-111-1-1000033−3−3−3−333000000000003−3−330000000
χ3822-2-222-1-22-2-222-111-2-211-1-12-1-1-211112-1-1-2-2211-1-12-2-1-111-111-1-2211-1-1-22001-11-1−333−3-2-22211-1-111-1-10000−3−33333−3−300000000000−333−30000000
χ3922-2-22-122-2-212-12-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1-111-1-11-1-111002-200002-22-2000000000000-1-111-1-111-1-1110003−333−3−300000000003−30
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χ4122-2-22-122-2-212-12-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1-111-1-11-1-11100-220000-22-2200000000000011-1-111-1-111-1-10003−333−3−30000000000−330
χ4222-2-22-122-2-212-12-2-2-2122-2-2-12-11-2-211-12-11212211-2-1-2-2-1-1-111-1-11-1-11100-220000-22-2200000000000011-1-111-1-111-1-1000−33−3−33300000000003−30
χ4322-2-2-122-221-2-122-2-21-2-2-222-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-111-1-12-2002-22-20000-1-111-1-111-1-11100000000000003−3003−33−3000000003−3000
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χ5044444-2-2-4-44-24-2-2-2-24-22222-2-21-2-2-211-2-21-2-4222-1-1-4222-1-1111122-1-1-1-1000000002323−23−230000000000000000−3−3−3−333330000000000000000000000
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χ534444-24-244-24-24-2-2-2-24-2-2-2-2-21-2-211-2-2-21-2-2-2411-2-2-2411-2-21111-2-211114400-2-2-2-20000-2-2-2-2111111110000000000000000000000000000000000
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χ604444-2-24-4-4-2-2-2-2444-2-2-4-4-4-41-2-21-2-2-2-21-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000-333-30000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.