Finite Group Databasebeta

← Group #13170636

Character table — Group #13170636

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size11222222222444444444444666666666666888889912121212121212121212121212181818181824242424363672721081122222222244444444444466666666666688888991212121212121212121212121218181818182424242436367272108
order12333466612123336661212121212128888242424242424242436121212442242424242424242424242424266121266662461242266646661212666666121212121212888824242424242424246612121244224242424242424242424242426612126666246124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-11111-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111111-11-1-11111111111111111111111111-1-11111-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111111-11-1-1
χ41111111111111111111111111-1-11111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111111111111111111111111-1-11111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111
χ511111111111111111111111-1-111-1-1-1-1111111111-1-11-1-1-1-1-1-1111111-1-1-1-1-11111-11-11-111111111111111111111111-1-111-1-1-1-1111111111-1-11-1-1-1-1-1-1111111-1-1-1-1-11111-11-11-1
χ611111111111111111111111-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1111111111111111111111111-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-11
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1
χ922222-2222-2-2222222-2-2-2-2-2-200000000000022-2-2-2220000000000000-2-2-22200000000022222-2222-2-2222222-2-2-2-2-2-200000000000022-2-2-2220000000000000-2-2-222000000000
χ1022222-2222-2-2222222-2-2-2-2-2-200000000000022-2-2-2-2-20000000000000222-2-200000000022222-2222-2-2222222-2-2-2-2-2-200000000000022-2-2-2-2-20000000000000222-2-2000000000
χ112222-12-122222-1-12-1-1-1222-1-1220022220000-1-1-1-1-1002-1-1-1-1-1-1000000000002-1-1-120-1002222-12-122222-1-12-1-1-1222-1-1220022220000-1-1-1-1-1002-1-1-1-1-1-1000000000002-1-1-120-100
χ122222-12-122222-1-12-1-1-1222-1-1220022220000-1-1-1-1-100-2-1-1-1-1-1-100000000000-2111-201002222-12-122222-1-12-1-1-1222-1-1220022220000-1-1-1-1-100-2-1-1-1-1-1-100000000000-2111-20100
χ132222-12-122222-1-12-1-1-1222-1-1-2-200-2-2-2-20000-1-1-1-1-1002111111000000000002-1-1-1-201002222-12-122222-1-12-1-1-1222-1-1-2-200-2-2-2-20000-1-1-1-1-1002111111000000000002-1-1-1-20100
χ142222-12-122222-1-12-1-1-1222-1-1-2-200-2-2-2-20000-1-1-1-1-100-211111100000000000-211120-1002222-12-122222-1-12-1-1-1222-1-1-2-200-2-2-2-20000-1-1-1-1-100-211111100000000000-211120-100
χ15222-1222-12-1-1-1-12-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-122022-1-1-1-122-1-1-1-12-1-1-1-1000000000222-1222-12-1-1-1-12-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-122022-1-1-1-122-1-1-1-12-1-1-1-1000000000
χ16222-1222-12-1-1-1-12-1-1222-1-1-1-122-2-2-1-1-1-11111-1-12-1-1-2-2022-1-1-1-1-2-21111-21111000000000222-1222-12-1-1-1-12-1-1222-1-1-1-122-2-2-1-1-1-11111-1-12-1-1-2-2022-1-1-1-1-2-21111-21111000000000
χ17222-1222-12-1-1-1-12-1-1222-1-1-1-1-2-2221111-1-1-1-1-1-12-1-1-2-20-2-2111122-1-1-1-1-21111000000000222-1222-12-1-1-1-12-1-1222-1-1-1-1-2-2221111-1-1-1-1-1-12-1-1-2-20-2-2111122-1-1-1-1-21111000000000
χ18222-1222-12-1-1-1-12-1-1222-1-1-1-1-2-2-2-211111111-1-12-1-1220-2-21111-2-211112-1-1-1-1000000000222-1222-12-1-1-1-12-1-1222-1-1-1-1-2-2-2-211111111-1-12-1-1220-2-21111-2-211112-1-1-1-1000000000
χ19222-12-22-1211-1-12-1-12-2-21111000033−3−333−3−3-1-1-2112200033−3−30033−3−3-211-1-1000000000222-12-22-1211-1-12-1-12-2-21111000033−3−333−3−3-1-1-2112200033−3−30033−3−3-211-1-1000000000
χ20222-12-22-1211-1-12-1-12-2-21111000033−3−3−3−333-1-1-211-2-200033−3−300−3−3332-1-111000000000222-12-22-1211-1-12-1-12-2-21111000033−3−3−3−333-1-1-211-2-200033−3−300−3−3332-1-111000000000
χ21222-12-22-1211-1-12-1-12-2-211110000−3−33333−3−3-1-1-211-2-2000−3−3330033−3−32-1-111000000000222-12-22-1211-1-12-1-12-2-211110000−3−33333−3−3-1-1-211-2-2000−3−3330033−3−32-1-111000000000
χ22222-12-22-1211-1-12-1-12-2-211110000−3−333−3−333-1-1-21122000−3−33300−3−333-211-1-1000000000222-12-22-1211-1-12-1-12-2-211110000−3−333−3−333-1-1-21122000−3−33300−3−333-211-1-1000000000
χ2322-122222-122-12-1-12-12-1-1-122002200002222-1-1-1-1-1002000000-1-1-1-1-1-100000-12-1-1020-1022-122222-122-12-1-12-12-1-1-122002200002222-1-1-1-1-1002000000-1-1-1-1-1-100000-12-1-1020-10
χ2422-122222-122-12-1-12-12-1-1-122002200002222-1-1-1-1-100-2000000-1-1-1-1-1-1000001-2110-201022-122222-122-12-1-12-12-1-1-122002200002222-1-1-1-1-100-2000000-1-1-1-1-1-1000001-2110-2010
χ2522-122222-122-12-1-12-12-1-1-12200-2-20000-2-2-2-2-1-1-1-1-100200000011111100000-12-1-10-201022-122222-122-12-1-12-12-1-1-12200-2-20000-2-2-2-2-1-1-1-1-100200000011111100000-12-1-10-2010
χ2622-122222-122-12-1-12-12-1-1-12200-2-20000-2-2-2-2-1-1-1-1-100-2000000111111000001-211020-1022-122222-122-12-1-12-12-1-1-12200-2-20000-2-2-2-2-1-1-1-1-100-2000000111111000001-211020-10
χ272-22220-2-2-200222-2-2-20000002−2−i2i22−22−2−i2i2−i2i22-20002i−2i02−22−22−2−i2i2−i2i2−i2i20002i−2i0000000002-22220-2-2-200222-2-2-20000002−2−i2i22−22−2−i2i2−i2i22-20002i−2i02−22−22−2−i2i2−i2i2−i2i20002i−2i000000000
χ282-22220-2-2-200222-2-2-20000002−2i2−i22−22−2i2−i2i2−i22-2000−2i2i02−22−22−2i2−i2i2−i2i2−i2000−2i2i0000000002-22220-2-2-200222-2-2-20000002−2i2−i22−22−2i2−i2i2−i22-2000−2i2i02−22−22−2i2−i2i2−i2i2−i2000−2i2i000000000
χ292-22220-2-2-200222-2-2-2000000−22−i2i2−22−22−i2i2−i2i22-2000−2i2i0−22−22−22−i2i2−i2i2−i2i2000−2i2i0000000002-22220-2-2-200222-2-2-2000000−22−i2i2−22−22−i2i2−i2i22-2000−2i2i0−22−22−22−i2i2−i2i2−i2i2000−2i2i000000000
χ302-22220-2-2-200222-2-2-2000000−22i2−i2−22−22i2−i2i2−i22-20002i−2i0−22−22−22i2−i2i2−i2i2−i20002i−2i0000000002-22220-2-2-200222-2-2-2000000−22i2−i2−22−22i2−i2i2−i22-20002i−2i0−22−22−22i2−i2i2−i2i2−i20002i−2i000000000
χ312-22-120-21-23−3-1-1211-2003−33−32−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7-1103−32i−2i02−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70−i3i3−ii0000000002-22-120-21-23−3-1-1211-2003−33−32−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7-1103−32i−2i02−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70−i3i3−ii000000000
χ322-22-120-21-23−3-1-1211-2003−33−32−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7-1103−3−2i2i02−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70i3−i3i−i0000000002-22-120-21-23−3-1-1211-2003−33−32−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7-1103−3−2i2i02−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70i3−i3i−i000000000
χ332-22-120-21-23−3-1-1211-2003−33−3−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7-1103−3−2i2i0−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70i3−i3i−i0000000002-22-120-21-23−3-1-1211-2003−33−3−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7-1103−3−2i2i0−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70i3−i3i−i000000000
χ342-22-120-21-23−3-1-1211-2003−33−3−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7-1103−32i−2i0−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70−i3i3−ii0000000002-22-120-21-23−3-1-1211-2003−33−3−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7-1103−32i−2i0−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70−i3i3−ii000000000
χ352-22-120-21-2−33-1-1211-200−33−332−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23-110−332i−2i02−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230i3−i3−ii0000000002-22-120-21-2−33-1-1211-200−33−332−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23-110−332i−2i02−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230i3−i3−ii000000000
χ362-22-120-21-2−33-1-1211-200−33−332−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23-110−33−2i2i02−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230−i3i3i−i0000000002-22-120-21-2−33-1-1211-200−33−332−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23-110−33−2i2i02−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230−i3i3i−i000000000
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χ534-444-202-4-4004-2-2-42200000022−220022−2222−220000-22000000−22−22−22000000000000000000004-444-202-4-4004-2-2-42200000022−220022−2222−220000-22000000−22−22−2200000000000000000000
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χ1284-4-2440-4-4200-24-22-4200000000−2i22i20000−2i22i2−2i22i2-22000000000000i2−i2i2−i2i2−i200000000000000-442-4-4044-2002-42-24-2000000002i2−2i200002i2−2i22i2−2i22-2000000000000−i2i2−i2i2−i2i200000000000000
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χ1388-8-4-4-40444−4343222-2-2-20023−2323−23000000000000-110−3300000000000000000000000000000-884440-4-4-443−43-2-2-222200−2323−23230000000000001-103−300000000000000000000000000000

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