Finite Group Databasebeta

← Group #11771553

Character table — Group #11771553

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888888888888888888888881818181818181818363636363636363636363636363636367272
order1222444433446666661212121212121212246666666612121212121212121212121212121212888888881616161616161616161616161616161688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−iii−i−ii−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26i−i
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−iii−i−ii−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26i−i
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii−i−iii−ii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ii
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii−i−iii−iiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ii
χ131111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111i−iii−i−ii−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ii
χ141111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111i−iii−i−ii−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ii
χ151111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111−ii−i−iii−ii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46i−i
χ161111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111−ii−i−iii−iiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46i−i
χ172222222222-2-2222222222222220000000000-2-2-2-2-2-2-2-20000000022-2-2-2-222000000000000000000
χ182222222222-2-2222222222222220000000000-2-2-2-2-2-2-2-200000000-2-22222-2-2000000000000000000
χ192222-2-2-2-222-22222222-2-2-2-2-2-2-2-20000000000-2-2-2-22222000000002i−2i−2i−2i2i2i2i−2i000000000000000000
χ202222-2-2-2-222-22222222-2-2-2-2-2-2-2-20000000000-2-2-2-2222200000000−2i2i2i2i−2i−2i−2i2i000000000000000000
χ2122-2-22i−2i2i−2i220022-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ460000000000ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ4100
χ2222-2-22i−2i2i−2i220022-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ460000000000−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ4100
χ2322-2-22i−2i2i−2i220022-2-2-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ460000000000ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ4100
χ2422-2-22i−2i2i−2i220022-2-2-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ460000000000−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ4100
χ2522-2-2−2i2i−2i2i220022-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000000000−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ4700
χ2622-2-2−2i2i−2i2i220022-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000000000ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ4700
χ2722-2-2−2i2i−2i2i220022-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000000000−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ4700
χ2822-2-2−2i2i−2i2i220022-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000000000ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ4700
χ292-2-2222-2-22200-2-2-2-22222-2-222-2-2000000000000000000000000002i−2i0000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ302-2-2222-2-22200-2-2-2-22222-2-222-2-2000000000000000000000000002i−2i0000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
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χ332-2-22-2-2222200-2-2-2-222-2-222-2-22200000000000000000000000000220000-2-2−i2i2i2−i2i2−i2−i2i20000000000
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χ352-2-22-2-2222200-2-2-2-222-2-222-2-22200000000000000000000000000-2-20000222−2−222−2−220000000000
χ362-2-22-2-2222200-2-2-2-222-2-222-2-22200000000000000000000000000-2-2000022−222−2−222−20000000000
χ37444444441-2441-21-21-21-21-21-21-2441111-2-2-2-211-2-211-2-21111-2-2-2-200000000000000000000000000
χ38444444441-2441-21-21-21-21-21-21-2-4-4-1-1-1-1222211-2-211-2-2-1-1-1-1222200000000000000000000000000
χ39444444441-2-4-41-21-21-21-21-21-21-20033-3-30000-1-122-1-12233-3-3000000000000000000000000000000
χ40444444441-2-4-41-21-21-21-21-21-21-200-3-3330000-1-122-1-122-3-333000000000000000000000000000000
χ4144444444-2144-21-21-21-21-21-21-2144-2-2-2-21111-2-211-2-211-2-2-2-2111100000000000000000000000000
χ4244444444-2144-21-21-21-21-21-21-21-4-42222-1-1-1-1-2-211-2-2112222-1-1-1-100000000000000000000000000
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χ4444444444-21-4-4-21-21-21-21-21-21-21000000-3-33322-1-122-1-10000-3-33300000000000000000000000000
χ454444-4-4-4-41-24-41-21-21-2-12-12-12-124-41111-2-2-2-211-2-2-1-122-1-1-1-1222200000000000000000000000000
χ464444-4-4-4-41-24-41-21-21-2-12-12-12-12-44-1-1-1-1222211-2-2-1-1221111-2-2-2-200000000000000000000000000
χ474444-4-4-4-41-2-441-21-21-2-12-12-12-120033-3-30000-1-12211-2-2-3-333000000000000000000000000000000
χ484444-4-4-4-41-2-441-21-21-2-12-12-12-1200-3-3330000-1-12211-2-233-3-3000000000000000000000000000000
χ494444-4-4-4-4-214-4-21-21-212-12-12-12-14-4-2-2-2-21111-2-21122-1-12222-1-1-1-100000000000000000000000000
χ504444-4-4-4-4-214-4-21-21-212-12-12-12-1-442222-1-1-1-1-2-21122-1-1-2-2-2-2111100000000000000000000000000
χ514444-4-4-4-4-21-44-21-21-212-12-12-12-100000033-3-322-1-1-2-2110000-3-33300000000000000000000000000
χ524444-4-4-4-4-21-44-21-21-212-12-12-12-1000000-3-33322-1-1-2-211000033-3-300000000000000000000000000
χ534-44-44i−4i−4i4i1-200-121-2-12i−2i−i2i−i2ii−2i00−i3i3−i3i300−2i32i33-3003i−3i003−33−30023−2300000000000000000000000000
χ544-44-44i−4i−4i4i1-200-121-2-12i−2i−i2i−i2ii−2i00−i3i3i3−i3−2i32i300-3300−3i3i003−3−3323−230000000000000000000000000000
χ554-44-44i−4i−4i4i1-200-121-2-12i−2i−i2i−i2ii−2i00i3−i3−i3i32i3−2i300-3300−3i3i00−333−3−23230000000000000000000000000000
χ564-44-44i−4i−4i4i1-200-121-2-12i−2i−i2i−i2ii−2i00i3−i3i3−i3002i3−2i33-3003i−3i00−33−3300−232300000000000000000000000000
χ574-44-44i−4i−4i4i4400-4-444-4-44i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ584-44-44i−4i−4i4i-21002-1-212-1−2ii2i−i2i−i−2ii0000−2i32i3−i3i3i3−i3003-3003i−3i0023−233−3−3300000000000000000000000000
χ594-44-44i−4i−4i4i-21002-1-212-1−2ii2i−i2i−i−2ii00002i3−2i3i3−i3−i3i3003-3003i−3i00−2323−333−300000000000000000000000000
χ604-44-44i−4i−4i4i-21002-1-212-1−2ii2i−i2i−i−2ii00−2i32i300i3−i3i3−i300-3300−3i3i23−2300−33−3300000000000000000000000000
χ614-44-44i−4i−4i4i-21002-1-212-1−2ii2i−i2i−i−2ii002i3−2i300−i3i3−i3i300-3300−3i3i−2323003−33−300000000000000000000000000
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χ644-44-4−4i4i4i−4i1-200-121-2-12−i2ii−2ii−2i−i2i00i3−i3−i3i32i3−2i300-33003i−3i003−3−3323−230000000000000000000000000000
χ654-44-4−4i4i4i−4i1-200-121-2-12−i2ii−2ii−2i−i2i00i3−i3i3−i3002i3−2i33-300−3i3i003−33−30023−2300000000000000000000000000
χ664-44-4−4i4i4i−4i4400-4-444-4-4−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
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χ684-44-4−4i4i4i−4i-21002-1-212-12i−i−2ii−2ii2i−i00002i3−2i3i3−i3−i3i3003-300−3i3i0023−233−3−3300000000000000000000000000
χ694-44-4−4i4i4i−4i-21002-1-212-12i−i−2ii−2ii2i−i00−2i32i300i3−i3i3−i300-33003i−3i−2323003−33−300000000000000000000000000
χ704-44-4−4i4i4i−4i-21002-1-212-12i−i−2ii−2ii2i−i002i3−2i300−i3i3−i3i300-33003i−3i23−2300−33−3300000000000000000000000000
χ7188-8-88i−8i8i−8i2-4002-4-24-242i−4i2i−4i−2i4i−2i4i0000000000000000000000000000000000000000000000000000
χ7288-8-88i−8i8i−8i-4200-424-24-2−4i2i−4i2i4i−2i4i−2i0000000000000000000000000000000000000000000000000000
χ7388-8-8−8i8i−8i8i2-4002-4-24-24−2i4i−2i4i2i−4i2i−4i0000000000000000000000000000000000000000000000000000
χ7488-8-8−8i8i−8i8i-4200-424-24-24i−2i4i−2i−4i2i−4i2i0000000000000000000000000000000000000000000000000000
χ758-8-8888-8-82-400-24-242-42-4-242-4-240000000000000000000000000000000000000000000000000000
χ768-8-8888-8-8-42004-24-2-42-424-2-424-20000000000000000000000000000000000000000000000000000
χ778-8-88-8-8882-400-24-242-4-242-4-242-40000000000000000000000000000000000000000000000000000
χ788-8-88-8-888-42004-24-2-424-2-424-2-420000000000000000000000000000000000000000000000000000

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