Finite Group Databasebeta

← Group #13156027

Character table — Group #13156027

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212181824242424242424242436363636363636363672727272216
order1222333446666666661212121233366666666612121212121212121212121236661212121212128888242424242424242424242424242424242424242424242424242424242424242444412121212121212124444412121212121212124
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
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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
χ11222222-122222-12-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200000000020000-1-1-1-100000
χ12222222-122222-12-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2000000000-20000111100000
χ13222222-122222-12-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2000000000-20000111100000
χ14222222-122222-12-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2111111112200000000020000-1-1-1-100000
χ15222222-1-2-2222-12-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−322000000000-20000-1-11100000
χ16222222-1-2-2222-12-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333-2-20000000002000011-1-100000
χ17222222-1-2-2222-12-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3-2-20000000002000011-1-100000
χ18222222-1-2-2222-12-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−3333322000000000-20000-1-11100000
χ1922222-122222-12-122-122222-12-1-1-122-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000002-1-122-1-1-1-1022000000-1-1000
χ2022222-122222-12-122-122222-12-1-1-122-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-211-2-211110-2-200000011000
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χ2222222-122222-12-122-122222-12-1-1-122-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2000011111111111100000000000000-211-2-21111022000000-1-1000
χ232222-12222-1-1222222-12222-1-12-1-1-1-122-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100222-1-1-1-1-1-100022000000-1-10
χ242222-12222-1-1222222-12222-1-12-1-1-1-122-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2111111000-2-2000000110
χ252222-12222-1-1222222-12222-1-12-1-1-1-122-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100222-1-1-1-1-1-1000-2-2000000110
χ262222-12222-1-1222222-12222-1-12-1-1-1-122-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100-2-2-211111100022000000-1-10
χ2722-2-2222002-22-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-20000002−22−22−22−22−22−222−2−222−2−222−2−222−2−222−2−222−2−22-2000000000000002-20000000
χ2822-2-2222002-22-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-20000002−2−222−22−2−22−2222−2−222−2−222−2−2−2−222−2−222−2−222-2200000000000000-220000000
χ2922-2-2222002-22-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-2000000−222−2−22−222−22−2−2−222−2−222−2−22222−2−222−2−222−2−2-2200000000000000-220000000
χ3022-2-2222002-22-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-2000000−22−22−22−22−22−22−2−222−2−222−2−222−2−222−2−222−2−2222-2000000000000002-20000000
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χ3322-2-222-1002-221-2-11-2-23−33−32-1-12-2-11-1111-2003−33−3003−33−3-1-1110033−3−3−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-22000000000000001-1−3300000
χ3422-2-222-1002-221-2-11-2-23−33−32-1-12-2-11-1111-2003−33−3003−33−3-1-1110033−3−3−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ232-200000000000000-113−300000
χ3522-2-222-1002-221-2-11-2-2−33−332-1-12-2-11-1111-200−33−3300−33−33-1-11100−3−3332−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ72-200000000000000-11−3300000
χ3622-2-222-1002-221-2-11-2-2−33−332-1-12-2-11-1111-200−33−3300−33−33-1-11100−3−3332−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-22000000000000001-13−300000
χ3722-2-222-1002-221-2-11-2-2−33−332-1-12-2-11-1111-200−33−3300−33−33-1-11100−3−333−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-22000000000000001-13−300000
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χ422-2-22222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2-2222-2-2-2-2-2-22222222-2-22-22-22-2200000000000000000000000000000000000000000000000000-22000000-220
χ432-2-222-122-2-2-212-1-2-21222-2-2-12-111-2-2112-1-1-1222-1-11-2-2-211-111-1-11-11-110000000000003−33−33−33−33−33−3000000000000000−i3i300−i3−i3i3i302i−2i000000−ii000
χ442-2-222-122-2-2-212-1-2-21222-2-2-12-111-2-2112-1-1-1222-1-11-2-2-211-111-1-11-11-110000000000003−33−33−33−33−33−3000000000000000i3−i300i3i3−i3−i30−2i2i000000i−i000
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χ1178-8-88-4-4-4-88444-4-4444-444-4-4222-2-2-2-2-2-222244-2-2-2-2-4-42222-111-1-221-11-10000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.