Finite Group Databasebeta

← Group #11772388

Character table — Group #11772388

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size1111111122222222222222222222222222224444444444444444444444444444444444444444444444444444444418181818181818181818181818181818242424242424242424242424242424242424242424242424
order122244442233446666668888888812121212121212123666666666661212121212121212121212122424242424242424242424242424242424242424242424242424242424242424161616161616161616161616161616168888888824242424242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i
χ61111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii
χ71111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ81111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ91-1-1111-1-11-111-11-1-1-1-1111111-1-1-1-111-1-111-1-1111-1-1-1-111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i
χ101-1-1111-1-11-111-11-1-1-1-1111111-1-1-1-111-1-111-1-1111-1-1-1-111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-1-111-1-111−i−iii−i−iii
χ111-1-1111-1-11-111-11-1-1-1-1111111-1-1-1-111-1-111-1-1111-1-1-1-111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii
χ121-1-1111-1-11-111-11-1-1-1-1111111-1-1-1-111-1-111-1-1111-1-1-1-111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-1-111-1-111ii−i−iii−i−i
χ131-1-11-1-111-1111-11-1-1-1-11111-1-111-1-1-1-111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1ii−i−i−i−iii-1-11111-1-1
χ141-1-11-1-111-1111-11-1-1-1-11111-1-111-1-1-1-111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11−i−iiiii−i−i11-1-1-1-111
χ151-1-11-1-111-1111-11-1-1-1-11111-1-111-1-1-1-111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111
χ161-1-11-1-111-1111-11-1-1-1-11111-1-111-1-1-1-111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1−i−iiiii−i−i-1-11111-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ1822222222222-12222-1-12-12222222222-1-1-1-122-12-12-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000022220000-1-1-1-1-1-1-1-100000000
χ1922222222222-12222-1-12-12222222222-1-1-1-122-12-12-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000-2-2-2-200001111111100000000
χ2022222222222-12222-1-12-1-2-2-2-2-2-2-2-222-1-1-1-122-12-12-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111-2-2111111-2-2111111000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2122222222222-12222-1-12-1-2-2-2-2-2-2-2-222-1-1-1-122-12-12-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111-2-2111111-2-2111111000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ222222222222-1222-1-122-1222222222-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000000000222200000000-1-1-1-1-1-1-1-1
χ232222222222-1222-1-122-1222222222-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000000000-2-2-2-20000000011111111
χ242222222222-1222-1-122-12-2-2-2-2-2-2-2-2-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12-1-111-2-2111111-2-2111111-2-2111111-2-2111100000000000000000000000000000000−i3i3−i3i3−i3i3−i3i3
χ252222222222-1222-1-122-12-2-2-2-2-2-2-2-2-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12-1-111-2-2111111-2-2111111-2-2111111-2-2111100000000000000000000000000000000i3−i3i3−i3i3−i3i3−i3
χ2622222222-2-222-2-222222200000000222222222-2-2-2-222-2-2-2-22-2-2-2-22222-2-2-2-20000000000000000000000000000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ2722222222-2-222-2-222222200000000222222222-2-2-2-222-2-2-2-22-2-2-2-22222-2-2-2-200000000000000000000000000000000−2−222−2−222−2−222−2−222000000000000000000000000
χ282222-2-2-2-22222-2-222222200000000-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022−2−222−2−2−2−222−2−222000000000000000000000000
χ292222-2-2-2-22222-2-222222200000000-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000−2−222−2−22222−2−222−2−2000000000000000000000000
χ302222-2-2-2-2-2-22222222222-2-22222-2-2-2-2-2-2-2-2-2-22-2-2-2-222-2-2-2-222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222220000000000000000000000000000000000000000
χ312222-2-2-2-2-2-22-12222-1-12-122-2-2-2-222-2-21111-2-2-1-21-21-1-11111-12-1-1-111112-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-211111100000000000000002i2i−2i−2i0000−i−i−i−iiiii00000000
χ322222-2-2-2-2-2-22-12222-1-12-122-2-2-2-222-2-21111-2-2-1-21-21-1-11111-12-1-1-111112-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-21111110000000000000000−2i−2i2i2i0000iiii−i−i−i−i00000000
χ332222-2-2-2-2-2-22-12222-1-12-1-2-22222-2-2-2-21111-2-2-1-21-21-1-11111-12-1-1-111112-1-1-1-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000003−33−3−33−3300000000
χ342222-2-2-2-2-2-22-12222-1-12-1-2-22222-2-2-2-21111-2-2-1-21-21-1-11111-12-1-1-111112-1-1-1-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000−33−333−33−300000000
χ352222-2-2-2-2-2-2-1222-1-122-1222-2-2-2-22211-2-2-2-211-11-21-2-1-11111-1-12-1-11111-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000000000002i2i−2i−2i00000000−i−i−i−iiiii
χ362222-2-2-2-2-2-2-1222-1-122-1222-2-2-2-22211-2-2-2-211-11-21-2-1-11111-1-12-1-11111-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-2111100000000000000000000−2i−2i2i2i00000000iiii−i−i−i−i
χ372222-2-2-2-2-2-2-1222-1-122-12-2-22222-2-211-2-2-2-211-11-21-2-1-11111-1-12-1-11111-12-1-111-2-2111111-2-21111-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000000000003−33−3−33−33
χ382222-2-2-2-2-2-2-1222-1-122-12-2-22222-2-211-2-2-2-211-11-21-2-1-11111-1-12-1-11111-12-1-111-2-2111111-2-21111-1-122-1-1-1-1-1-122-1-1-1-100000000000000000000000000000000−33−333−33−3
χ3922-2-22i−2i2i−2i0022002-22-2-2-22−2−i2i2−i2i22−22i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i00002−22−222−2−22−22−222−2−2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−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−ζ47000000000000000000000000
χ4022-2-22i−2i2i−2i0022002-22-2-2-22−2−i2i2−i2i22−22i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i00002−22−222−2−22−22−222−2−2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2ζ25+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+ζ47000000000000000000000000
χ4122-2-22i−2i2i−2i0022002-22-2-2-2−22i2−i2i2−i2−222i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i0000−22−22−2−222−22−22−2−222i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2ζ11+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+ζ43000000000000000000000000
χ4222-2-22i−2i2i−2i0022002-22-2-2-2−22i2−i2i2−i2−222i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i0000−22−22−2−222−22−22−2−222i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2−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−ζ43000000000000000000000000
χ4322-2-2−2i2i−2i2i0022002-22-2-2-22−2i2−i2i2−i22−2−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i00002−22−222−2−22−22−222−2−2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2−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−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+ζ47000000000000000000000000
χ4422-2-2−2i2i−2i2i0022002-22-2-2-22−2i2−i2i2−i22−2−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i00002−22−222−2−22−22−222−2−2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2ζ25+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+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−ζ47000000000000000000000000
χ4522-2-2−2i2i−2i2i0022002-22-2-2-2−22−i2i2−i2i2−22−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i0000−22−22−2−222−22−22−2−222−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2ζ11+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−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−ζ43000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.