Finite Group Databasebeta

← Group #10706159

Character table — Group #10706159

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122234444444444666888888881212121224668888121212121212121212122424242424242424242424242424242416161616161616161616161616161616444412121212121212128888
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
χ51111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1ii−i−i
χ61111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−i−iii
χ71111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−iii
χ81111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-11111ii−i−i
χ911111-1-111-1-111-1-11111111-1-1-1-11111-11-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ1011111-1-111-1-111-1-11111111-1-1-1-11111-11-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ1111111-1-111-1-111-1-11111111-1-1-1-11111-11-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ1211111-1-111-1-111-1-11111111-1-1-1-11111-11-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ1311111-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-11
χ1411111-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-111-1
χ1511111-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111-111-1
χ1611111-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-11-1-11
χ17222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222-2-2-2-2-2-22220000000022222-222000022-2-2-2-2-2-2-2-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ19222222222-2-2-2-2-2-22220000000022222-222000022-2-2-2-2-2-2-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ202222222-2-22222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ212222222-2-2-2-2-2-22222200000000-2-2-2-2-22-2-2000022-2-22222-2-2000000000000000022−2−222−2−2−2−222−2−2220000000000000000
χ222222222-2-2-2-2-2-22222200000000-2-2-2-2-22-2-2000022-2-22222-2-20000000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222-2-22222-2-222222000000002222-2-2-2-20000-2-222-2-222-2-2000000000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2422222-2-22222-2-222222000000002222-2-2-2-20000-2-222-2-222-2-20000000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2522222-2-222-2-222-2-2222-2-2-2-222222222-22-2-2-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2622222-2-2-2-222-2-2-2-222200000000-2-2-2-222220000-2-22222-2-2-2-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2722222-2-2-2-222-2-2-2-222200000000-2-2-2-222220000-2-22222-2-2-2-20000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-22-222-2-222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ292222-12222222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ302222-12222222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ312222-12222222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ322222-12222222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ332222-122-2-22222-2-2-1-1-1222222221111-2-211-2-2-2-2-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ342222-122-2-22222-2-2-1-1-1222222221111-2-211-2-2-2-2-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ352222-122-2-22222-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2112222-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ362222-122-2-22222-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2112222-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ372222-1-2-222-2-222-2-2-1-1-12222-2-2-2-2-1-1-1-1-221122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-1110000
χ382222-1-2-222-2-222-2-2-1-1-12222-2-2-2-2-1-1-1-1-221122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-10000
χ392222-1-2-222-2-222-2-2-1-1-1-2-2-2-22222-1-1-1-1-2211-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ402222-1-2-222-2-222-2-2-1-1-1-2-2-2-22222-1-1-1-1-2211-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ412222-1-2-2-2-2-2-22222-1-1-12222-2-2-2-211112-2-1-1-2-222111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ422222-1-2-2-2-2-2-22222-1-1-12222-2-2-2-211112-2-1-1-2-222111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ432222-1-2-2-2-2-2-22222-1-1-1-2-2-2-2222211112-2-1-122-2-2111111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ442222-1-2-2-2-2-2-22222-1-1-1-2-2-2-2222211112-2-1-122-2-2111111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ452-22-22002i−2i2-2002i−2i-22-2−i2−i2i2i2−i2−i2i2i22i2i−2i−2i00002−22−2002-2002i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ470000000000000000
χ462-22-22002i−2i2-2002i−2i-22-2−i2−i2i2i2−i2−i2i2i22i2i−2i−2i00002−22−2002-2002i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ470000000000000000
χ472-22-22002i−2i2-2002i−2i-22-2i2i2−i2−i2i2i2−i2−i22i2i−2i−2i0000−22−22002-2002i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ430000000000000000
χ482-22-22002i−2i2-2002i−2i-22-2i2i2−i2−i2i2i2−i2−i22i2i−2i−2i0000−22−22002-2002i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ430000000000000000
χ492-22-22002i−2i-2200−2i2i-22-2−i2−i2i2i2i2i2−i2−i22i2i−2i−2i00002−2−2200-2200−2i2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ430000000000000000
χ502-22-22002i−2i-2200−2i2i-22-2−i2−i2i2i2i2i2−i2−i22i2i−2i−2i00002−2−2200-2200−2i2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i2ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ430000000000000000
χ512-22-22002i−2i-2200−2i2i-22-2i2i2−i2−i2−i2−i2i2i22i2i−2i−2i0000−222−200-2200−2i2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i2ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ470000000000000000
χ522-22-22002i−2i-2200−2i2i-22-2i2i2−i2−i2−i2−i2i2i22i2i−2i−2i0000−222−200-2200−2i2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ470000000000000000
χ532-22-2200−2i2i2-200−2i2i-22-2−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i0000−22−22002-200−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ470000000000000000
χ542-22-2200−2i2i2-200−2i2i-22-2−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i0000−22−22002-200−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ470000000000000000
χ552-22-2200−2i2i2-200−2i2i-22-2i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i00002−22−2002-200−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43−ζ13−ζ29+ζ31+ζ47ζ13+ζ29−ζ31−ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ43−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47ζ11−ζ25−ζ41+ζ43−ζ11+ζ25+ζ41−ζ430000000000000000
χ562-22-2200−2i2i2-200−2i2i-22-2i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i00002−22−2002-200−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43−ζ11−ζ25−ζ41−ζ43ζ11+ζ25+ζ41+ζ43ζ13+ζ29−ζ31−ζ47−ζ13−ζ29+ζ31+ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ43ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47ζ13+ζ29+ζ31+ζ47−ζ13−ζ29−ζ31−ζ47−ζ11+ζ25+ζ41−ζ43ζ11−ζ25−ζ41+ζ430000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.