Finite Group Databasebeta

← Group #10713388

Character table — Group #10713388

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1244888822234446888888121224242424666121212242424242424224444666688888812121212121212122424242424242424242424241616161616161616161616161616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11-11-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11-11-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ131111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ1722222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-22-2-2-2-1-11122-2-2-2-2-1-1111111-1-1-1-11111111100000000000000000000
χ1922222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-22-2-211-1-1-2-222-2-211-1-111111111-1-1-1-1111100000000000000000000
χ2022222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-2221111-1-1-1-111111111-1-1-1-100000000000000000000
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χ2622222222-2-222-2-222-2-2-2-222222222-2-22-2-22-2-2-2-2220000-2200000000-220000-2-22200000000-2-22200000000000000000000
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χ322222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-11111112-22-222-1-111-2-222-2-2-1-111-1-1-1-11111-1-1-1-1111100000000000000000000
χ332222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-1111111-22-222211-1-122-2-2-2-211-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ342222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-1111111-2-2-2-2-2-2111122222211111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ352222-2-2-2-22-2-222-2-22-2-2222222-2-2-2-22-2-22-2-2-2-222220000000000000000000000000000000000000000000000002-2-220000
χ362222-2-2-2-22-2-222-2-22-2-2222222-2-2-2-22-2-22-2-2-2-22222000000000000000000000000000000000000000000000000-222-20000
χ372222-2-2-2-2-22-22-22-2222-2-22222-2-2-2-2-22-2-22-222-2-222000000000000000000000000000000000000000000002-2-2200000000
χ382222-2-2-2-2-22-22-22-2222-2-22222-2-2-2-2-22-2-22-222-2-22200000000000000000000000000000000000000000000-222-200000000
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χ4622-2-22i2i−2i−2i2222-2-2-222i−2i2i−2i2i−2i-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46
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χ4822-2-22i2i−2i−2i2-2-22-22222i−2i−2i2i−2i2i-2-22i2i−2i−2i2-2-2-2222i−2i−2i2i−2i2i-202000-2-200−2i2i000022000000−2i2i−2i2i0000000000000000000000000000
χ4922-2-22i2i−2i−2i2-2-2-1-222-12i−2i−2i2i−2i2i11−i−iii-1111-1-1−iii−ii−i20-2000-1-1−i3i32i−2i000011i3−i33−33−3−ii−ii3−33−3−i3i3−i3i300000000000000000000
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χ5822-2-22i2i−2i−2i-22-2-12-22-1−2i2i2i−2i−2i2i11−i−iii1-11-11-1i−i−iii−i0-20200i3−i31100−2i2i00−i3i3-1-13−3−33−333−3i−i−ii−i3i3i3−i300000000000000000000
χ5922-2-22i2i−2i−2i-2-22222-22−2i2i−2i2i2i−2i-2-22i2i−2i−2i-2-2222-2−2i2i−2i2i2i−2i0000000000000000000000000000000000002ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ46−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26000000000000
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χ77444444444-4-4-24-4-4-244-4-4-4-4-2-2-2-2-2-2-222-222-2-2222200000000000000000000000000000000000000000000000000000000
χ7844444444-44-4-2-44-4-2-4-444-4-4-2-2-2-2-2-22-222-2222-2-22200000000000000000000000000000000000000000000000000000000
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χ8344-4-4−4i−4i4i4i444-2-4-4-4-2−4i4i−4i4i−4i4i222i2i−2i−2i-2-2-22222i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000
χ8444-4-4−4i−4i4i4i-4-44-244-4-24i−4i4i−4i−4i4i222i2i−2i−2i22-2-2-22−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000000000000000
χ854-44i−4i4ζ14+4ζ46−4ζ14−4ζ46−4ζ10−4ζ264ζ10+4ζ260004000-40000004i−4i4ζ14+4ζ46−4ζ14−4ζ46−4ζ10−4ζ264ζ10+4ζ260000000000000000000000000000000000000000000000002ζ11+2ζ43−2ζ11−2ζ43−2ζ31−2ζ472ζ31+2ζ47−2ζ13−2ζ292ζ13+2ζ29−2ζ25−2ζ412ζ25+2ζ41000000000000
χ864-44i−4i4ζ14+4ζ46−4ζ14−4ζ46−4ζ10−4ζ264ζ10+4ζ260004000-40000004i−4i4ζ14+4ζ46−4ζ14−4ζ46−4ζ10−4ζ264ζ10+4ζ26000000000000000000000000000000000000000000000000−2ζ11−2ζ432ζ11+2ζ432ζ31+2ζ47−2ζ31−2ζ472ζ13+2ζ29−2ζ13−2ζ292ζ25+2ζ41−2ζ25−2ζ41000000000000
χ874-44i−4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ260004000-40000004i−4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ26000000000000000000000000000000000000000000000000−2ζ31−2ζ472ζ31+2ζ47−2ζ11−2ζ432ζ11+2ζ432ζ25+2ζ41−2ζ25−2ζ41−2ζ13−2ζ292ζ13+2ζ29000000000000
χ884-44i−4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ260004000-40000004i−4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ260000000000000000000000000000000000000000000000002ζ31+2ζ47−2ζ31−2ζ472ζ11+2ζ43−2ζ11−2ζ43−2ζ25−2ζ412ζ25+2ζ412ζ13+2ζ29−2ζ13−2ζ29000000000000
χ894-4−4i4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ460004000-4000000−4i4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ46000000000000000000000000000000000000000000000000−2ζ13−2ζ292ζ13+2ζ292ζ25+2ζ41−2ζ25−2ζ412ζ11+2ζ43−2ζ11−2ζ432ζ31+2ζ47−2ζ31−2ζ47000000000000
χ904-4−4i4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ460004000-4000000−4i4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ460000000000000000000000000000000000000000000000002ζ13+2ζ29−2ζ13−2ζ29−2ζ25−2ζ412ζ25+2ζ41−2ζ11−2ζ432ζ11+2ζ43−2ζ31−2ζ472ζ31+2ζ47000000000000
χ914-4−4i4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ460004000-4000000−4i4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ46000000000000000000000000000000000000000000000000−2ζ25−2ζ412ζ25+2ζ41−2ζ13−2ζ292ζ13+2ζ292ζ31+2ζ47−2ζ31−2ζ47−2ζ11−2ζ432ζ11+2ζ43000000000000
χ924-4−4i4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ460004000-4000000−4i4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ460000000000000000000000000000000000000000000000002ζ25+2ζ41−2ζ25−2ζ412ζ13+2ζ29−2ζ13−2ζ29−2ζ31−2ζ472ζ31+2ζ472ζ11+2ζ43−2ζ11−2ζ43000000000000
χ938-88i−8i8ζ14+8ζ46−8ζ14−8ζ46−8ζ10−8ζ268ζ10+8ζ26000-40004000000−4i4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ2600000000000000000000000000000000000000000000000000000000000000000000
χ948-88i−8i−8ζ14−8ζ468ζ14+8ζ468ζ10+8ζ26−8ζ10−8ζ26000-40004000000−4i4i4ζ14+4ζ46−4ζ14−4ζ46−4ζ10−4ζ264ζ10+4ζ2600000000000000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i−8ζ10−8ζ268ζ10+8ζ268ζ14+8ζ46−8ζ14−8ζ46000-400040000004i−4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ4600000000000000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i8ζ10+8ζ26−8ζ10−8ζ26−8ζ14−8ζ468ζ14+8ζ46000-400040000004i−4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ4600000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.