Finite Group Databasebeta

← Group #13138734

Character table — Group #13138734

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222224444446666666666666666666612121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order12442346888812126122424242433666612121212121224242424242424243666612121212122424242424242424242424241616161616161616484848484848484848484848484848482244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511-1-1-1111-1-111-1-1-1111-1-111-1-111-1-1-1-111-1-1-1-111111-1-1-11-1-1111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ611-1-1-1111-1-111-1-1-1111-1-111-1-111-1-1-1-111-1-1-1-111111-1-1-11-1-1111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711-1-1-1111-1-111-1-1-1111-1-111-1-111-1-1-1-111-1-1-1-111111-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811-1-1-1111-1-111-1-1-1111-1-111-1-111-1-1-1-111-1-1-1-111111-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222-1222-122-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000020200-1-100-1-1
χ10222222222222222222222-1222-122-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-200110011
χ1122222222222222222222-12-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1222222222222222222222-12-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ1322222222-2-2-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1422222222-2-2-2-22222-2-2-2-22-1222-122-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000000000−i3i300−i3i3
χ1522222222-2-2-2-22222-2-2-2-22-1222-122-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000000000i3−i300i3−i3
χ1622222222-2-2-2-22222-2-2-2-2-12-1-1-12-1-122-1-111111111-12-1-1-1-1-12-1-1-2-21111-2-21111000000003333−3−3−3−33333−3−3−3−3000000000000
χ1722222222-2-2-2-22222-2-2-2-2-12-1-1-12-1-122-1-111111111-12-1-1-1-1-12-1-1-2-21111-2-2111100000000−3−3−3−33333−3−3−3−33333000000000000
χ182222-22-22000022-2-2000022-2-2222222-2-2000000002-2-2-2222-2-2-200000000000022−2−222−2−222−2−222−2−222−2−222−2−2000000000000
χ192222-22-22000022-2-2000022-2-2222222-2-2000000002-2-2-2222-2-2-2000000000000−2−222−2−222−2−222−2−222−2−222−2−222000000000000
χ202222-22-22000022-2-20000-1211-12-1-1221133−3−333−3−3-1-211-1-1-1-2110033−3−30033−3−322−2−222−2−2ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46000000000000
χ212222-22-22000022-2-20000-1211-12-1-1221133−3−333−3−3-1-211-1-1-1-2110033−3−30033−3−3−2−222−2−222−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46000000000000
χ222222-22-22000022-2-20000-1211-12-1-12211−3−333−3−333-1-211-1-1-1-21100−3−33300−3−33322−2−222−2−2ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14000000000000
χ232222-22-22000022-2-20000-1211-12-1-12211−3−333−3−333-1-211-1-1-1-21100−3−33300−3−333−2−222−2−222−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14000000000000
χ2422-2-222-220000-2-22-20000222222-2-2-2-2-2-20000000022222-2-2-2-2-200000000000022−2−2−2−22222−2−222−2−2−2−222−2−222000000000000
χ2522-2-222-220000-2-22-20000222222-2-2-2-2-2-20000000022222-2-2-2-2-2000000000000−2−22222−2−2−2−222−2−22222−2−222−2−2000000000000
χ2622-2-222-220000-2-22-20000-12-1-1-1211-2-21133−3−3−3−333-12-1-1-111-21100−3−3330033−3−322−2−2−2−222ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14000000000000
χ2722-2-222-220000-2-22-20000-12-1-1-1211-2-21133−3−3−3−333-12-1-1-111-21100−3−3330033−3−3−2−22222−2−2−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14000000000000
χ2822-2-222-220000-2-22-20000-12-1-1-1211-2-211−3−33333−3−3-12-1-1-111-2110033−3−300−3−33322−2−2−2−222ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46000000000000
χ2922-2-222-220000-2-22-20000-12-1-1-1211-2-211−3−33333−3−3-12-1-1-111-2110033−3−300−3−333−2−22222−2−2−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46000000000000
χ3022-2-2-222222-2-2-2-2-22-2-22222-2-222-2-2-2-2222222-2-2-2-22-2-2-22-2-2222-2-2-2-2-2-2222222000000000000000000000000000000000000
χ3122-2-2-222222-2-2-2-2-22-2-2222-1-2-22-1-2-211222222-2-2-2-2-1111-111-1-1-1111111-1-1-1-1-1-1000000000000000000000000000000−i3i300i3−i3
χ3222-2-2-222222-2-2-2-2-22-2-2222-1-2-22-1-2-211222222-2-2-2-2-1111-111-1-1-1111111-1-1-1-1-1-1000000000000000000000000000000i3−i300−i3i3
χ3322-2-2-222222-2-2-2-2-22-2-222-1211-1211-2-2-1-1-1-1-1-11111-1-211-1112-1-1-2-2111122-1-1-1-1000000003333−3−3−3−3−3−3−3−33333000000000000
χ3422-2-2-222222-2-2-2-2-22-2-222-1211-1211-2-2-1-1-1-1-1-11111-1-211-1112-1-1-2-2111122-1-1-1-100000000−3−3−3−333333333−3−3−3−3000000000000
χ3522-2-2-2222-2-222-2-2-2222-2-22-1-2-22-1-2-21122-2-2-2-22222-1111-111-1-1-1-1-1-1-1-1-1111111000000000000000000000000020-200-1-10011
χ3622-2-2-2222-2-222-2-2-2222-2-22-1-2-22-1-2-21122-2-2-2-22222-1111-111-1-1-1-1-1-1-1-1-11111110000000000000000000000000-202001100-1-1
χ3722-2-2-2222-2-222-2-2-2222-2-2-1211-1211-2-2-1-11111-1-1-1-1-1-211-1112-1-122-1-1-1-1-2-211112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ3822-2-2-2222-2-222-2-2-2222-2-2-1211-1211-2-2-1-11111-1-1-1-1-1-211-1112-1-122-1-1-1-1-2-21111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ392-22i−2i020-2−i2i22−22i−2i002−2−i2i22200-2-22i−2i2i−2i00−i2i2−i2i22−22−22000-22i−2i0002−22−22−2−i2i2−i2i2−i2i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000000000
χ402-22i−2i020-2−i2i22−22i−2i002−2−i2i22200-2-22i−2i2i−2i00−i2i2−i2i22−22−22000-22i−2i0002−22−22−2−i2i2−i2i2−i2i2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000000000
χ412-22i−2i020-2−i2i22−22i−2i002−2−i2i2-12−i3i31-2−ii2i−2i3−3ζ10+ζ14−ζ10−ζ14ζ26+ζ46−ζ26−ζ46ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ14-10−i3i31−ii03−32−2ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ14−i2i2ζ10+ζ14−ζ10−ζ14ζ26+ζ46−ζ26−ζ46−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ31+ζ41ζ31−ζ41ζ29−ζ43−ζ29+ζ43ζ25−ζ47−ζ25+ζ47−ζ11+ζ13ζ11−ζ13−ζ29−ζ43ζ29+ζ43ζ31+ζ41−ζ31−ζ41−ζ11−ζ13ζ11+ζ13ζ25+ζ47−ζ25−ζ47000000000000
χ422-22i−2i020-2−i2i22−22i−2i002−2−i2i2-12−i3i31-2−ii2i−2i3−3ζ10+ζ14−ζ10−ζ14ζ26+ζ46−ζ26−ζ46ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ14-10−i3i31−ii03−32−2ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ14−i2i2ζ10+ζ14−ζ10−ζ14ζ26+ζ46−ζ26−ζ46ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ31−ζ41−ζ31+ζ41−ζ29+ζ43ζ29−ζ43−ζ25+ζ47ζ25−ζ47ζ11−ζ13−ζ11+ζ13ζ29+ζ43−ζ29−ζ43−ζ31−ζ41ζ31+ζ41ζ11+ζ13−ζ11−ζ13−ζ25−ζ47ζ25+ζ47000000000000
χ432-22i−2i020-2−i2i22−22i−2i002−2−i2i2-12i3−i31-2−ii2i−2i−33ζ26+ζ46−ζ26−ζ46ζ10+ζ14−ζ10−ζ14ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46-10i3−i31−ii0−332−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46−i2i2ζ26+ζ46−ζ26−ζ46ζ10+ζ14−ζ10−ζ14−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25−ζ47−ζ25+ζ47−ζ11+ζ13ζ11−ζ13−ζ31+ζ41ζ31−ζ41ζ29−ζ43−ζ29+ζ43−ζ11−ζ13ζ11+ζ13ζ25+ζ47−ζ25−ζ47−ζ29−ζ43ζ29+ζ43ζ31+ζ41−ζ31−ζ41000000000000
χ442-22i−2i020-2−i2i22−22i−2i002−2−i2i2-12i3−i31-2−ii2i−2i−33ζ26+ζ46−ζ26−ζ46ζ10+ζ14−ζ10−ζ14ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46-10i3−i31−ii0−332−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46−i2i2ζ26+ζ46−ζ26−ζ46ζ10+ζ14−ζ10−ζ14ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25+ζ47ζ25−ζ47ζ11−ζ13−ζ11+ζ13ζ31−ζ41−ζ31+ζ41−ζ29+ζ43ζ29−ζ43ζ11+ζ13−ζ11−ζ13−ζ25−ζ47ζ25+ζ47ζ29+ζ43−ζ29−ζ43−ζ31−ζ41ζ31+ζ41000000000000
χ452-22i−2i020-2i2−i2−222i−2i00−22i2−i22200-2-22i−2i2i−2i00i2−i2i2−i2−22−222000-22i−2i000−22−22−22i2−i2i2−i2i2−i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000000000
χ462-22i−2i020-2i2−i2−222i−2i00−22i2−i22200-2-22i−2i2i−2i00i2−i2i2−i2−22−222000-22i−2i000−22−22−22i2−i2i2−i2i2−i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000000000
χ472-22i−2i020-2i2−i2−222i−2i00−22i2−i2-12−i3i31-2−ii2i−2i3−3−ζ10−ζ14ζ10+ζ14−ζ26−ζ46ζ26+ζ46−ζ26+ζ46ζ26−ζ46−ζ10+ζ14ζ10−ζ14-10−i3i31−ii03−3−22−ζ26+ζ46ζ26−ζ46−ζ10+ζ14ζ10−ζ14i2−i2−ζ10−ζ14ζ10+ζ14−ζ26−ζ46ζ26+ζ46ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ29−ζ43−ζ29+ζ43ζ31−ζ41−ζ31+ζ41−ζ11+ζ13ζ11−ζ13−ζ25+ζ47ζ25−ζ47ζ31+ζ41−ζ31−ζ41ζ29+ζ43−ζ29−ζ43ζ25+ζ47−ζ25−ζ47ζ11+ζ13−ζ11−ζ13000000000000
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χ9512-1212i−12i0-606−6i26i262−62−6i6i00−32323i2−3i2000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212i−12i0-6066i2−6i2−6262−6i6i0032−32−3i23i2000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12−12i12i0-606−6i26i2−62626i−6i0032−323i2−3i2000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12−12i12i0-6066i2−6i262−626i−6i00−3232−3i23i2000000000000000000000000000000000000000000000000000000000000000000000000000000

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