Finite Group Databasebeta

← Group #10950930

Character table — Group #10950930

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222222344444466666668888888824666688881212121212121212242424242424242424242424242424241616161616161616161616161616161622446666121212122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-11111-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-11-1-11
χ6111111-1-11111-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-111-1
χ7111111-1-11111-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-111-1
χ8111111-1-11111-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1111-1-11
χ91111-1-11111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-11-1-111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ101111-1-11111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-11-1-111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111
χ111111-1-11111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-11-1-111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ121111-1-11111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-11-1-111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ131111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111-1-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1111-11-1
χ141111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111-1-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-11-11
χ151111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111-1-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111-11-11
χ161111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111-1-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-11-11-1
χ172222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222-2-2-2-2-2-22222222000000002-222220000-2-2-2-2-2-2-2-2000000000000000022−2−222−2−222−2−222−2−20000000000000000
χ19222222222-2-2-2-2-2-22222222000000002-222220000-2-2-2-2-2-2-2-20000000000000000−2−222−2−222−2−222−2−2220000000000000000
χ2022222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2122222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2222222222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2322222222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ24222222-2-22222-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-22222222-2-2-2-22-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ25222222-2-22-2-2-222-22-2-2-2-22200000000-2222-2-20000-2-2-22222-2000000000000000022−2−222−2−2−2−222−2−2220000000000000000
χ26222222-2-22-2-2-222-22-2-2-2-22200000000-2222-2-20000-2-2-22222-20000000000000000−2−222−2−22222−2−222−2−20000000000000000
χ27222222-2-2-1222-2-22-11111-1-122222222-2-2-1-111-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ28222222-2-2-1222-2-22-11111-1-122222222-2-2-1-111-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ29222222-2-2-1222-2-22-11111-1-1-2-2-2-2-2-2-2-2-2-2-1-1112222-1-1-11111-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ30222222-2-2-1222-2-22-11111-1-1-2-2-2-2-2-2-2-2-2-2-1-1112222-1-1-11111-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ312222-2-22222-2-2-2-2222222222222-2-2-2-2-22-2-2-2-2-2-2222-2-222-2-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ322222-2-2222-22222-2222222200000000-2-2-2-2-2-20000-222-2-222-2000000000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ332222-2-2222-22222-2222222200000000-2-2-2-2-2-20000-222-2-222-20000000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ342222-2-222-12-2-2-2-22-1-1-1-1-1-1-12222-2-2-2-2-221111-2-222-111-1-111-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ352222-2-222-12-2-2-2-22-1-1-1-1-1-1-12222-2-2-2-2-221111-2-222-111-1-111-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ362222-2-222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-2-22222-22111122-2-2-111-1-111-1-1-1-1-11111-1-1-1-11111000000000000000022-2-2-1-1-1-111110000
χ372222-2-222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-2-22222-22111122-2-2-111-1-111-1-1-1-1-11111-1-1-1-111110000000000000000-2-2221111-1-1-1-10000
χ382222-2-2-2-222-2-22222-2-2-2-2222222-2-2-2-22-2-2-22222-2-22-2-2-2-2222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ392222-2-2-2-22-222-2-2-22-2-2-2-2220000000022-2-2220000-22222-2-2-2000000000000000022−2−2−2−222−2−22222−2−20000000000000000
χ402222-2-2-2-22-222-2-2-22-2-2-2-2220000000022-2-2220000-22222-2-2-20000000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ412222-2-2-2-2-12-2-2222-11111-1-12222-2-2-2-22-211-1-122-2-2-11111-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ422222-2-2-2-2-12-2-2222-11111-1-12222-2-2-2-22-211-1-122-2-2-11111-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ432222-2-2-2-2-12-2-2222-11111-1-1-2-2-2-222222-211-1-1-2-222-11111-1-1-1-1-1-1-111111111-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ442222-2-2-2-2-12-2-2222-11111-1-1-2-2-2-222222-211-1-1-2-222-11111-1-1-1-1-1-1-111111111-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ4522-2-2002-2202i−2i2i−2i0222-2-2-2-2−i2−i2i2i222−2−20000002−2−i2i202i−2i002i−2i022−2−2−i2−i2i2i222−2−2−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−ζ43−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−ζ430000000000000000
χ4622-2-2002-2202i−2i2i−2i0222-2-2-2-2−i2−i2i2i222−2−20000002−2−i2i202i−2i002i−2i022−2−2−i2−i2i2i222−2−2−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+ζ43ζ25−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+ζ430000000000000000
χ4722-2-2002-2202i−2i2i−2i0222-2-2-2-2i2i2−i2−i2−2−222000000−22i2−i202i−2i002i−2i0−2−222i2i2−i2−i2−2−222i2i2−i2−i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000000000000000
χ4822-2-2002-2202i−2i2i−2i0222-2-2-2-2i2i2−i2−i2−2−222000000−22i2−i202i−2i002i−2i0−2−222i2i2−i2−i2−2−222i2i2−i2−i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000000000000000
χ4922-2-2002-220−2i2i−2i2i0222-2-2-2-2−i2−i2i2i2−2−222000000−22−i2i20−2i2i00−2i2i0−2−222−i2−i2i2i2−2−222−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−ζ47ζ11−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−ζ470000000000000000
χ5022-2-2002-220−2i2i−2i2i0222-2-2-2-2−i2−i2i2i2−2−222000000−22−i2i20−2i2i00−2i2i0−2−222−i2−i2i2i2−2−222−i2−i2i2i2−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+ζ47−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+ζ470000000000000000
χ5122-2-2002-220−2i2i−2i2i0222-2-2-2-2i2i2−i2−i222−2−20000002−2i2−i20−2i2i00−2i2i022−2−2i2i2−i2−i222−2−2i2i2−i2−i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000000000000000
χ5222-2-2002-220−2i2i−2i2i0222-2-2-2-2i2i2−i2−i222−2−20000002−2i2−i20−2i2i00−2i2i022−2−2i2i2−i2−i222−2−2i2i2−i2−i2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000000000000000
χ5322-2-200-22202i−2i−2i2i02-2-222-2-2−i2−i2i2i222−2−2000000−22i2−i202i−2i00−2i2i022−2−2−i2−i2i2i2−2−222i2i2−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−ζ43ζ25−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+ζ430000000000000000
χ5422-2-200-22202i−2i−2i2i02-2-222-2-2−i2−i2i2i222−2−2000000−22i2−i202i−2i00−2i2i022−2−2−i2−i2i2i2−2−222i2i2−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+ζ43−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−ζ430000000000000000
χ5522-2-200-22202i−2i−2i2i02-2-222-2-2i2i2−i2−i2−2−2220000002−2−i2i202i−2i00−2i2i0−2−222i2i2−i2−i222−2−2−i2−i2i2i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−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−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000000000000000
χ5622-2-200-22202i−2i−2i2i02-2-222-2-2i2i2−i2−i2−2−2220000002−2−i2i202i−2i00−2i2i0−2−222i2i2−i2−i222−2−2−i2−i2i2i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11+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−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000000000000000
χ5722-2-200-2220−2i2i2i−2i02-2-222-2-2−i2−i2i2i2−2−2220000002−2i2−i20−2i2i002i−2i0−2−222−i2−i2i2i222−2−2i2i2−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−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+ζ470000000000000000
χ5822-2-200-2220−2i2i2i−2i02-2-222-2-2−i2−i2i2i2−2−2220000002−2i2−i20−2i2i002i−2i0−2−222−i2−i2i2i222−2−2i2i2−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+ζ47ζ11−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−ζ470000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.