Finite Group Databasebeta

← Group #13156417

Character table — Group #13156417

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212181824242424242424242436363636363636363672727272216
order12223334466666666612121212333666666666121212121212121212121212366612121212121288882424242424242424242424242424242424242424242424242424242424242424224121212121212121244444661212121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111111-1-1-111-1-1-1-1-1-111-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000022000000000-2000022-2-200000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000-2-200000000020000-2-22200000
χ11222222-122-1-12222-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200000000020000-1-1-1-100000
χ12222222-122-1-12222-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2000000000-20000111100000
χ13222222-122-1-12222-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2000000000-20000111100000
χ14222222-122-1-12222-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2111111112200000000020000-1-1-1-100000
χ15222222-1-2-2-1-12222-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−322000000000-20000-1-11100000
χ16222222-1-2-2-1-12222-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333-2-20000000002000011-1-100000
χ17222222-1-2-2-1-12222-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3-2-20000000002000011-1-100000
χ18222222-1-2-2-1-12222-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−3333322000000000-20000-1-11100000
χ1922222-1222222-12-122-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100222-1-1-1-1-1-100022000000-1-10
χ2022222-1222222-12-122-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2111111000-2-2000000110
χ2122222-1222222-12-122-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100222-1-1-1-1-1-1000-2-2000000110
χ2222222-1222222-12-122-12222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100-2-2-211111100022000000-1-10
χ232222-1222222-12-122-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000002-1-122-1-1-1-1022000000-1-1000
χ242222-1222222-12-122-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-211-2-211110-2-200000011000
χ252222-1222222-12-122-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000111111111111000000000000002-1-122-1-1-1-10-2-200000011000
χ262222-1222222-12-122-122222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2000011111111111100000000000000-211-2-21111022000000-1-1000
χ2722-2-2222002-2-2-222-2-2-20000222-22-22-2-2-2-2200000000000022-2-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-2000000000000002-20000000
χ2822-2-2222002-2-2-222-2-2-20000222-22-22-2-2-2-2200000000000022-2-2000000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-2200000000000000-220000000
χ2922-2-2222002-2-2-222-2-2-20000222-22-22-2-2-2-2200000000000022-2-2000000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-2200000000000000-220000000
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χ3122-2-222-100-11-2-2221-2-233−3−32-1-1-2-11-11-2112003−33−3003−33−3-1-1110033−3−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ232-200000000000000-113−300000
χ3222-2-222-100-11-2-2221-2-233−3−32-1-1-2-11-11-2112003−33−3003−33−3-1-1110033−3−3−i2i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23-22000000000000001-1−3300000
χ3322-2-222-100-11-2-2221-2-233−3−32-1-1-2-11-11-2112003−33−3003−33−3-1-1110033−3−3i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23-22000000000000001-1−3300000
χ3422-2-222-100-11-2-2221-2-233−3−32-1-1-2-11-11-2112003−33−3003−33−3-1-1110033−3−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ232-200000000000000-113−300000
χ3522-2-222-100-11-2-2221-2-2−3−3332-1-1-2-11-11-211200−33−3300−33−33-1-11100−3−333−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ72-200000000000000-11−3300000
χ3622-2-222-100-11-2-2221-2-2−3−3332-1-1-2-11-11-211200−33−3300−33−33-1-11100−3−333−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7-22000000000000001-13−300000
χ3722-2-222-100-11-2-2221-2-2−3−3332-1-1-2-11-11-211200−33−3300−33−33-1-11100−3−333i2−i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7-22000000000000001-13−300000
χ3822-2-222-100-11-2-2221-2-2−3−3332-1-1-2-11-11-211200−33−3300−33−33-1-11100−3−333i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ72-200000000000000-11−3300000
χ392-22-22222-2-2-222-2-22-2-22-22-2222-2-2-2-2-2222-22-222-2-2-22-2-2222-2-222-22-22-2000000000000000000000000000000000000000000000000002i−2i0000002i−2i0
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χ412-22-2222-22-2-222-2-22-2-2-22-22222-2-2-2-2-2222-2-22-2-2222-222-2-22-2-22-22-22-220000000000000000000000000000000000000000000000002i−2i0000002i−2i000
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χ472-22-2-122-22-2-2-121-221-2-22-22-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-11-11-1000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000003−3003−33−302i−2i000000−ii000
χ482-22-2-122-22-2-2-121-221-2-22-22-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-11-11-1000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000−3300−33−330−2i2i000000i−i000
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χ594444-24-2-4-4-2-2-24-24-2-242222-21-2-211-2-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-100002323−23−2300000000−3−3−3−333330000000000000000000000000000000000000
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χ614444-2-244444-2-2-2-24-2-244441-2-21-2-2-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000004-2-2-2-2111100000000000000
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χ644444-2-24-4-444-2-2-2-24-2-2-4-4-4-41-2-21-2-2-2-21-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000000-333-300000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.