Finite Group Databasebeta

← Group #13156502

Character table — Group #13156502

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212181824242424242424242436363636363636363672727272216
order12223334466666666612121212333666666666121212121212121212121212366612121212121288882424242424242424242424242424242424242424242424242424242424242424444121212121212121224444661212121212124
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000022000000000-20000-2-22200000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000-2-20000000002000022-2-200000
χ11222222-12222-1-122-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200000000020000-1-1-1-100000
χ12222222-12222-1-122-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2000000000-20000111100000
χ13222222-12222-1-122-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2000000000-20000111100000
χ14222222-12222-1-122-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2111111112200000000020000-1-1-1-100000
χ15222222-1-2-222-1-122-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−322000000000-2000011-1-100000
χ16222222-1-2-222-1-122-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333-2-200000000020000-1-11100000
χ17222222-1-2-222-1-122-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3-2-200000000020000-1-11100000
χ18222222-1-2-222-1-122-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−3333322000000000-2000011-1-100000
χ1922222-12222-1222-122-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100222-1-1-1-1-1-100022000000-1-10
χ2022222-12222-1222-122-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2111111000-2-2000000110
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χ2222222-12222-1222-122-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100-2-2-211111100022000000-1-10
χ232222-12222-1222-122-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000002-1-122-1-1-1-1022000000-1-1000
χ242222-12222-1222-122-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-211-2-211110-2-200000011000
χ252222-12222-1222-122-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000111111111111000000000000002-1-122-1-1-1-10-2-200000011000
χ262222-12222-1222-122-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2000011111111111100000000000000-211-2-21111022000000-1-1000
χ2722-2-22222-2-2-2-2-2222-2-222-2-2222-2-2-2-2-2-22222-222-2-2-22-2-2222-2-222-222-2-20000000000000000000000000000000000000000000000002i−2i0000002i−2i000
χ2822-2-22222-2-2-2-2-2222-2-222-2-2222-2-2-2-2-2-22222-222-2-2-22-2-2222-2-222-222-2-2000000000000000000000000000000000000000000000000−2i2i000000−2i2i000
χ2922-2-2222-22-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2222-22-2-2222-222-2-22-2-22-22-2-222000000000000000000000000000000000000000000000000002i−2i0000002i−2i0
χ3022-2-2222-22-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2222-22-2-2222-222-2-22-2-22-22-2-22200000000000000000000000000000000000000000000000000−2i2i000000−2i2i0
χ3122-2-22-12-22-21-2-22-12-21-2-222-12-111-2-2112-1-1-2-1-2-2-1-1212211-111-11-111-1-100000000000000000000000033−3−333−3−333−3−300000−i3i3−i3−i3i3i30002i−2i000000−ii0
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χ3422-2-22-12-22-21-2-22-12-21-2-222-12-111-2-2112-1-1-2-1-2-2-1-1212211-111-11-111-1-1000000000000000000000000−3−333−3−333−3−33300000i3−i3i3i3−i3−i30002i−2i000000−ii0
χ3522-2-2-1222-21-2-2-2-1221-222-2-2-1-121111-2-2-12-1-1-2-1-1-2-2121122-111-1-11-1-11100000000000033−3−333−3−333−3−3000000000000000−i3i300−i3i3−i3i302i−2i000000−ii000
χ3622-2-2-1222-21-2-2-2-1221-222-2-2-1-121111-2-2-12-1-1-2-1-1-2-2121122-111-1-11-1-11100000000000033−3−333−3−333−3−3000000000000000i3−i300i3−i3i3−i30−2i2i000000i−i000
χ3722-2-2-1222-21-2-2-2-1221-222-2-2-1-121111-2-2-12-1-1-2-1-1-2-2121122-111-1-11-1-111000000000000−3−333−3−333−3−333000000000000000−i3i300−i3i3−i3i30−2i2i000000i−i000
χ3822-2-2-1222-21-2-2-2-1221-222-2-2-1-121111-2-2-12-1-1-2-1-1-2-2121122-111-1-11-1-111000000000000−3−333−3−333−3−333000000000000000i3−i300i3−i3i3−i302i−2i000000−ii000
χ392-2-22222002-22-2-2-2-2-2200002222-22-22-2-2-2-200000000000022-2-20000002−2−i2i22−22−2−i2i2−i2i22−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22i−2i00000000000000002i−2i00000
χ402-2-22222002-22-2-2-2-2-2200002222-22-22-2-2-2-200000000000022-2-20000002−2i2−i22−22−2i2−i2i2−i22−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−2i2i0000000000000000−2i2i00000
χ412-2-22222002-22-2-2-2-2-2200002222-22-22-2-2-2-200000000000022-2-2000000−22−i2i2−22−22−i2i2−i2i2−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−2i2i0000000000000000−2i2i00000
χ422-2-22222002-22-2-2-2-2-2200002222-22-22-2-2-2-200000000000022-2-2000000−22i2−i2−22−22i2−i2i2−i2−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22i−2i00000000000000002i−2i00000
χ432-2-2222-1002-2-11-2-21-223−33−32-1-12-2-11-1111-2003−33−3003−33−3-1-111003−33−32−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ72−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ72i−2i00000000000000−i3i3−ii00000
χ442-2-2222-1002-2-11-2-21-223−33−32-1-12-2-11-1111-2003−33−3003−33−3-1-111003−33−32−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ72−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−2i2i00000000000000i3−i3i−i00000
χ452-2-2222-1002-2-11-2-21-223−33−32-1-12-2-11-1111-2003−33−3003−33−3-1-111003−33−3−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−2i2i00000000000000i3−i3i−i00000
χ462-2-2222-1002-2-11-2-21-223−33−32-1-12-2-11-1111-2003−33−3003−33−3-1-111003−33−3−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ72i−2i00000000000000−i3i3−ii00000
χ472-2-2222-1002-2-11-2-21-22−33−332-1-12-2-11-1111-200−33−3300−33−33-1-11100−33−332−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ232−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232i−2i00000000000000i3−i3−ii00000
χ482-2-2222-1002-2-11-2-21-22−33−332-1-12-2-11-1111-200−33−3300−33−33-1-11100−33−332−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ232−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−2i2i00000000000000−i3i3i−i00000
χ492-2-2222-1002-2-11-2-21-22−33−332-1-12-2-11-1111-200−33−3300−33−33-1-11100−33−33−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−2i2i00000000000000−i3i3i−i00000
χ502-2-2222-1002-2-11-2-21-22−33−332-1-12-2-11-1111-200−33−3300−33−33-1-11100−33−33−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232i−2i00000000000000i3−i3−ii00000
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χ614444-2-2444-2-244-2-24-2-244441-2-211-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000004-2-2-2-2111100000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.