Finite Group Databasebeta

← Group #13159378

Character table — Group #13159378

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122222222222222222222224444444444444444444444444444444466668888888888888888888888888888888899991212121212121212121212121212121212121818181818182424242424242424363636363636363654545454108108
order1222333334466666666666666633334466666666666612121212121212121212121212128888121212121212121212121212121212121212121212121212121212121212121244444424242424242424242424242424242424441212121212121212121212122266661212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111111111-1-1111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1
χ91-1-11111111-111111-1-1-1-1-1-1-1-1-1-11111i−i-1-1-1-11111-1-1-1-11-1-1-1-1-1ii−i−i111111-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−ii−i11111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−i1-111-1-1i−iii−i−i1-1
χ101-1-11111111-111111-1-1-1-1-1-1-1-1-1-11111i−i-1-1-1-11111-1-1-1-11-1-1-1-1-1ii−i−i111111-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iiii−i11111111-1-1-1-1-1-1-1-1−ii−i−iiiiiii−i−i−i−i-11-1-111−ii−i−iii-11
χ111-1-11111111-111111-1-1-1-1-1-1-1-1-1-11111i−i-1-1-1-11111-1-1-1-11-1-1-1-1-1ii−i−i1111-1-111iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i−ii-1-1-1-1-1-1-1-111111111i−iii−i−i−i−i−i−iiiii1-111-1-1i−i−i−iii-11
χ121-1-11111111-111111-1-1-1-1-1-1-1-1-1-11111i−i-1-1-1-11111-1-1-1-11-1-1-1-1-1ii−i−i1111-1-111iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−ii-1-1-1-1-1-1-1-111111111−ii−i−iii−i−i−i−iiiii-11-1-111−iiii−i−i1-1
χ131-1-11111111-111111-1-1-1-1-1-1-1-1-1-11111−ii-1-1-1-11111-1-1-1-11-1-1-1-1-1−i−iii111111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−ii11111111-1-1-1-1-1-1-1-1i−iii−i−i−i−i−i−iiiii-11-1-111i−iii−i−i-11
χ141-1-11111111-111111-1-1-1-1-1-1-1-1-1-11111−ii-1-1-1-11111-1-1-1-11-1-1-1-1-1−i−iii111111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−ii11111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii1-111-1-1−ii−i−iii1-1
χ151-1-11111111-111111-1-1-1-1-1-1-1-1-1-11111−ii-1-1-1-11111-1-1-1-11-1-1-1-1-1−i−iii1111-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−ii−i-1-1-1-1-1-1-1-111111111i−iii−i−iiiii−i−i−i−i-11-1-111i−i−i−iii1-1
χ161-1-11111111-111111-1-1-1-1-1-1-1-1-1-11111−ii-1-1-1-11111-1-1-1-11-1-1-1-1-1−i−iii1111-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iiii−i-1-1-1-1-1-1-1-111111111−ii−i−iiiiiii−i−i−i−i1-111-1-1−iiii−i−i-11
χ17222222222-2-2222222222222222222200222222222222-2-2-2-2-2-20000-2-2-2-2000000000000-2-2-2-2-2-2-2-200000000000000002222000000000000000000-2-2222200000000000000-2-2000000
χ18222222222-2-2222222222222222222200222222222222-2-2-2-2-2-20000-2-2-2-2000000000000-2-2-2-2-2-2-2-20000000000000000-2-2-2-200000000000000000022-2-2-2-20000000000000022000000
χ1922222222-1222222-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-12222000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000000022-1-1-1-10000000022-1-1-1-1-1-1000000
χ2022222222-1222222-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-12222000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000000-2-2111100000000-2-2111111000000
χ2122222222-1222222-122222222-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1-1-1-1-1-12222-1111122220000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111222200000000000000000022-1-1-1-100000000-2-21111-1-1000000
χ2222222222-1222222-122222222-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1-1-1-1-1-12222-1111122220000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2000000000000000000-2-211110000000022-1-1-1-111000000
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χ2622222222-1-2-22222-122222222-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-11-2-2-2-21i3−i3i3−i3-2-2-2-200000000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-2-2-2-20000000000000000002211110000000000−i3i3−i3i3-1-1000000
χ2722222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-1222-1-1-12-1-1-12-1-1-122-1-1-1222222-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-100002222-1-1-1-1-1-122-1-1-1-1-1-10000002-1-1-12-1-1-100000000000000
χ2822222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-1222-1-1-12-1-1-12-1-1-122-1-1-1222222-1-1-1-2-2-2-22-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-10000-2-2-2-2111111-2-2111111000000-2111-211100000000000000
χ2922222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-1-2-22-1-1-12-1-1-12-1-1-122-1-1-12-2-2-2-22-1-1-12222-2111-21112-1-1-12-1-1-1-2111-2111-2111-21110000-2-222-1-1-1-1-1-122-1-1-1-1-1-1000000-2111-211100000000000000
χ3022222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-1-2-22-1-1-12-1-1-12-1-1-122-1-1-12-2-2-2-22-1-1-1-2-2-2-2-2111-21112-1-1-12-1-1-1-2111-2111-2111-2111000022-2-2111111-2-21111110000002-1-1-12-1-1-100000000000000
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χ322222-12-1-1222-12-1-12-12-1-1-12-1-122-12-1-122-12-1-1-12-1-1-12-1-12-12-1-122222-12-1-1-2-2-2-2-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-10000-2-211-2-2111111-2-211110000001-2111-21100000000000000
χ332222-12-1-1222-12-1-12-12-1-1-12-1-122-12-1-1-2-2-12-1-1-12-1-1-12-1-12-12-1-12-2-2-2-2-12-1-122221-2111-211-12-1-1-12-1-11-2111-2111-2111-2110000-2-2-1-122-1-1-1-1-1-122-1-1-1-10000001-2111-21100000000000000
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χ1214-4-444-2-2-2-2-444-2-2-2-2-4222-422222-2111002-1-1-1-21112-1-1-124-2-2-2-2−232323−23-42220000000000002-1-1-1-2111−2333323−3−3−323−3−3−3−2333300000000000000000000000000000000000000000000000000
χ1224-4-44-24-2-24-44-24-2-242-4222-422-4-4-24-2-2002-422-24-2-22-422-4-24-2-2400002-4220000000000002-422-24-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1234-4-44-24-2-2-24-4-24-2-2-22-4222-422221-2114i−4i-12-1-11-211-12-1-1-22-4222−2i−2i2i2i-24-2-20000−2i4i−2i−2i2i−4i2i2i1-211-12-1-1i−2iiii−2iii−i2i−i−i−i2i−i−i00000000000000000000000000000000000000000000000000
χ1244-4-44-24-2-2-24-4-24-2-2-22-4222-422221-211−4i4i-12-1-11-211-12-1-1-22-42222i2i−2i−2i-24-2-200002i−4i2i2i−2i4i−2i−2i1-211-12-1-1−i2i−i−i−i2i−i−ii−2iiii−2iii00000000000000000000000000000000000000000000000000
χ1254-4-44-24-2-2-2-44-24-2-2-22-4222-422221-21100-12-1-11-211-12-1-12-24-2-2-223−23−23232-422000000000000-12-1-11-211−323−3−33−23333−2333−323−3−300000000000000000000000000000000000000000000000000
χ1264-4-44-24-2-2-2-44-24-2-2-22-4222-422221-21100-12-1-11-211-12-1-12-24-2-2-2−232323−232-422000000000000-12-1-11-2113−2333−323−3−3−323−3−33−233300000000000000000000000000000000000000000000000000
χ1274-4-44-2-24-24-44-2-24-2422-4222-42-4-4-2-24-20022-42-2-24-222-42-4-2-24-24000022-4200000000000022-42-2-24-2000000000000000000000000000000000000000000000000000000000000000000
χ1284-4-44-2-24-2-24-4-2-24-2-222-4222-422211-214i−4i-1-12-111-21-1-12-1-222-422−2i−2i2i2i-2-24-20000−2i−2i4i−2i2i2i−4i2i11-21-1-12-1ii−2iiii−2ii−i−i2i−i−i−i2i−i00000000000000000000000000000000000000000000000000
χ1294-4-44-2-24-2-24-4-2-24-2-222-4222-422211-21−4i4i-1-12-111-21-1-12-1-222-4222i2i−2i−2i-2-24-200002i2i−4i2i−2i−2i4i−2i11-21-1-12-1−i−i2i−i−i−i2i−iii−2iiii−2ii00000000000000000000000000000000000000000000000000
χ1304-4-44-2-24-2-2-44-2-24-2-222-4222-422211-2100-1-12-111-21-1-12-12-2-24-2-223−23−232322-42000000000000-1-12-111-21−3−323−333−23333−233−3−323−300000000000000000000000000000000000000000000000000
χ1314-4-44-2-24-2-2-44-2-24-2-222-4222-422211-2100-1-12-111-21-1-12-12-2-24-2-2−232323−2322-42000000000000-1-12-111-2133−233−3−323−3−3−323−333−23300000000000000000000000000000000000000000000000000
χ1324-4-44-2-2-244-44-2-2-244222-4222-4-4-4-2-2-2400222-4-2-2-24222-4-4-2-2-2440000222-4000000000000222-4-2-2-24000000000000000000000000000000000000000000000000000000000000000000
χ1334-4-44-2-2-24-24-4-2-2-24-2222-4222-422111-24i−4i-1-1-12111-2-1-1-12-2222-42−2i−2i2i2i-2-2-240000−2i−2i−2i4i2i2i2i−4i111-2-1-1-12iii−2iiii−2i−i−i−i2i−i−i−i2i00000000000000000000000000000000000000000000000000
χ1344-4-44-2-2-24-24-4-2-2-24-2222-4222-422111-2−4i4i-1-1-12111-2-1-1-12-2222-422i2i−2i−2i-2-2-2400002i2i2i−4i−2i−2i−2i4i111-2-1-1-12−i−i−i2i−i−i−i2iiii−2iiii−2i00000000000000000000000000000000000000000000000000
χ1354-4-44-2-2-24-2-44-2-2-24-2222-4222-422111-200-1-1-12111-2-1-1-122-2-2-24-223−23−2323222-4000000000000-1-1-12111-2−3−3−323333−23333−23−3−3−32300000000000000000000000000000000000000000000000000
χ1364-4-44-2-2-24-2-44-2-2-24-2222-4222-422111-200-1-1-12111-2-1-1-122-2-2-24-2−232323−23222-4000000000000-1-1-12111-2333−23−3−3−323−3−3−323333−2300000000000000000000000000000000000000000000000000
χ13788-8-88-4-4-4-400-844448-4-4-4-84444-4-4222004-2-2-24-2-2-2-42220000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13888-8-8-48-4-4-4004-8444-48-4-44-8444-42-42200-24-2-2-24-2-22-4220000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13988-8-8-4-48-4-40044-844-4-48-444-844-422-4200-2-24-2-2-24-222-420000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14088-8-8-4-4-48-400444-84-4-4-48444-84-4222-400-2-2-24-2-2-24222-40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1418-88-88-4-4-4-400-84444-84448-4-4-4-44-422200-42224-2-2-24-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1428-88-8-48-4-4-4004-84444-844-48-4-4-442-422002-422-24-2-2-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1438-88-8-4-48-4-40044-84444-84-4-48-4-4422-420022-42-2-24-2-2-24-20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1448-88-8-4-4-48-400444-84444-8-4-4-48-44222-400222-4-2-2-24-2-2-240000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).