Finite Group Databasebeta

← Group #10950823

Character table — Group #10950823

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order12223444444666888824448888881212121212122424242416161616161616166121212242424242424161616161616161616161616444412121212121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-11-11-1
χ6111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-11-11
χ7111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-11-11
χ8111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1111-11-1
χ911111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1111111111111111-1-11-1-111-1-1-1-1-1-11111-1-1-1-11-1-11-1-11111-1-11-1-11
χ1011111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1111111111111111-1-11-1-111-1-1-1-1-1-11111-1-1-1-1-111-111-1-1-1-111-111-1
χ1111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-111-1-11111-1-1-1-111111-1-11-1-11111-1-1-111-1
χ1211111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-111-1-11111-1-1-1-11111-111-111-1-1-1-1111-1-11
χ1311111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-111111111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ1411111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-111111111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111
χ1511111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-111
χ1611111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ1722222222222222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-2000000002222-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000-2-2-2-2-2-222220000000000000000000000000000
χ192222222-2-2-2-222200002-22-200000022-2-2-2-200002222−2−2−2−222-2-200000022−2−222−2−222−2−20000000000000000
χ202222222-2-2-2-222200002-22-200000022-2-2-2-20000−2−2−2−2222222-2-2000000−2−222−2−222−2−2220000000000000000
χ212222222-2-2-2-22220000-22-2200000022-2-2-2-200002222−2−2−2−2-2-22200000022−2−2−2−222−2−2220000000000000000
χ222222222-2-2-2-22220000-22-2200000022-2-2-2-20000−2−2−2−22222-2-222000000−2−22222−2−222−2−20000000000000000
χ2322222-2-222-2-222200002-2-22000000-2-222-2-200002222−2−2−2−22-22-2000000−2−22222−2−2−2−2220000000000000000
χ2422222-2-222-2-222200002-2-22000000-2-222-2-20000−2−2−2−222222-22-200000022−2−2−2−22222−2−20000000000000000
χ2522222-2-222-2-22220000-222-2000000-2-222-2-200002222−2−2−2−2-22-22000000−2−222−2−22222−2−20000000000000000
χ2622222-2-222-2-22220000-222-2000000-2-222-2-20000−2−2−2−22222-22-2200000022−2−222−2−2−2−2220000000000000000
χ2722222-2-2-2-222222-2-2-2-222-2-222-2-222-2-2-2-222-2-2-2-2000000002-2-2222-2-2220000000000000000000000000000
χ2822222-2-2-2-222222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-200000000-222-22222-2-20000000000000000000000000000
χ292222-1222222-1-1-122222222222222-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ302222-1222222-1-1-122222222222222-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ312222-1222222-1-1-12222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000001111-1-111110000000000002-22-2-1-111-1-1110000
χ322222-1222222-1-1-12222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000001111-1-11111000000000000-22-2211-1-111-1-10000
χ332222-1222222-1-1-1-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1111100000000-1-1-1-11111110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ342222-1222222-1-1-1-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1111100000000-1-1-1-11111110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ352222-1222222-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-1111100000000111111-1-1-1-10000000000000000−i3i3i3−i3−i3i3i3−i30000
χ362222-1222222-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-1111100000000111111-1-1-1-10000000000000000i3−i3−i3i3i3−i3−i3i30000
χ372222-1-2-2-2-222-1-1-1222222-2-2-2-222-2-21111-1-1-1-1-1-100000000-111-111-1-1110000000000002-2-2211-1-1-1-1110000
χ382222-1-2-2-2-222-1-1-1222222-2-2-2-222-2-21111-1-1-1-1-1-100000000-111-111-1-111000000000000-222-2-1-11111-1-10000
χ392222-1-2-2-2-222-1-1-12222-2-222-2-2-2-2221111-1-1-1-1-1-1000000001-1-111111-1-100000000000022-2-21111-1-1-1-10000
χ402222-1-2-2-2-222-1-1-12222-2-222-2-2-2-2221111-1-1-1-1-1-1000000001-1-111111-1-1000000000000-2-222-1-1-1-111110000
χ412222-1-2-2-2-222-1-1-1-2-2-2-222-2-222-2-2221111-1-1111100000000-111-1-1-111-1-10000000000000000−i3i3i3−i3i3−i3−i3i30000
χ422222-1-2-2-2-222-1-1-1-2-2-2-222-2-222-2-2221111-1-1111100000000-111-1-1-111-1-10000000000000000i3−i3−i3i3−i3i3i3−i30000
χ432222-1-2-2-2-222-1-1-1-2-2-2-2-2-2222222-2-21111-1-11111000000001-1-11-1-1-1-1110000000000000000−i3i3−i3i3i3−i3i3−i30000
χ442222-1-2-2-2-222-1-1-1-2-2-2-2-2-2222222-2-21111-1-11111000000001-1-11-1-1-1-1110000000000000000i3−i3i3−i3−i3i3−i3i30000
χ4522-2-222i−2i2i−2i2-2-2-2200000000002i−2i2-22i−2i2i−2i2-2000022−2−222−2−20000002i−2i2-2−i2i2−i2i2−i2i2−i2i22−22−20000000000000000
χ4622-2-222i−2i2i−2i2-2-2-2200000000002i−2i2-22i−2i2i−2i2-20000−2−222−2−2220000002i−2i2-2i2−i2i2−i2i2−i2i2−i2−22−220000000000000000
χ4722-2-222i−2i2i−2i2-2-2-220000000000−2i2i-222i−2i2i−2i2-2000022−2−222−2−2000000−2i2i-22−i2i2−i2i2i2−i2i2−i2−22−220000000000000000
χ4822-2-222i−2i2i−2i2-2-2-220000000000−2i2i-222i−2i2i−2i2-20000−2−222−2−222000000−2i2i-22i2−i2i2−i2−i2i2−i2i22−22−20000000000000000
χ4922-2-222i−2i−2i2i-22-2-2222-2-200002i−2i00002i−2i−2i2i-2222-2-20000000000002i−2i000000002i−2i−2i2i-222-20000000000000000
χ5022-2-222i−2i−2i2i-22-2-2222-2-200002i−2i00002i−2i−2i2i-2222-2-20000000000002i−2i00000000−2i2i2i−2i2-2-220000000000000000
χ5122-2-222i−2i−2i2i-22-2-22-2-2220000−2i2i00002i−2i−2i2i-22-2-22222-2-2-2-2220000−2i2i0000−2i2i2i−2i000000000000000000000000
χ5222-2-222i−2i−2i2i-22-2-22-2-2220000−2i2i00002i−2i−2i2i-22-2-222-2-22222-2-20000−2i2i00002i−2i−2i2i000000000000000000000000
χ5322-2-22−2i2i2i−2i-22-2-2222-2-20000−2i2i0000−2i2i2i−2i-2222-2-2000000000000−2i2i000000002i−2i−2i2i2-2-220000000000000000
χ5422-2-22−2i2i2i−2i-22-2-2222-2-20000−2i2i0000−2i2i2i−2i-2222-2-2000000000000−2i2i00000000−2i2i2i−2i-222-20000000000000000
χ5522-2-22−2i2i2i−2i-22-2-22-2-22200002i−2i0000−2i2i2i−2i-22-2-22222-2-2-2-22200002i−2i00002i−2i−2i2i000000000000000000000000
χ5622-2-22−2i2i2i−2i-22-2-22-2-22200002i−2i0000−2i2i2i−2i-22-2-222-2-22222-2-200002i−2i0000−2i2i2i−2i000000000000000000000000
χ5722-2-22−2i2i−2i2i2-2-2-2200000000002i−2i-22−2i2i−2i2i2-2000022−2−222−2−20000002i−2i-22i2−i2i2−i2−i2i2−i2i2−22−220000000000000000
χ5822-2-22−2i2i−2i2i2-2-2-2200000000002i−2i-22−2i2i−2i2i2-20000−2−222−2−2220000002i−2i-22−i2i2−i2i2i2−i2i2−i22−22−20000000000000000
χ5922-2-22−2i2i−2i2i2-2-2-220000000000−2i2i2-2−2i2i−2i2i2-2000022−2−222−2−2000000−2i2i2-2i2−i2i2−i2i2−i2i2−i22−22−20000000000000000
χ6022-2-22−2i2i−2i2i2-2-2-220000000000−2i2i2-2−2i2i−2i2i2-20000−2−222−2−222000000−2i2i2-2−i2i2−i2i2−i2i2−i2i2−22−220000000000000000
χ614444-244-4-4-4-4-2-2-200004-44-4000000-2-22222000000000000-2-2220000000000000000000000000000000000
χ624444-244-4-4-4-4-2-2-20000-44-44000000-2-2222200000000000022-2-20000000000000000000000000000000000
χ634444-2-4-444-4-4-2-2-200004-4-4400000022-2-222000000000000-22-220000000000000000000000000000000000
χ644444-2-4-444-4-4-2-2-20000-444-400000022-2-2220000000000002-22-20000000000000000000000000000000000
χ6544-4-4-24i−4i4i−4i4-422-200000000004i−4i4-4−2i2i−2i2i-22000000000000000000−2i2i-220000000000000000000000000000
χ6644-4-4-24i−4i4i−4i4-422-20000000000−4i4i-44−2i2i−2i2i-220000000000000000002i−2i2-20000000000000000000000000000
χ6744-4-4-24i−4i−4i4i-4422-244-4-400004i−4i0000−2i2i2i−2i2-2-2-222000000000000−2i2i00000000000000000000000000000000
χ6844-4-4-24i−4i−4i4i-4422-2-4-4440000−4i4i0000−2i2i2i−2i2-222-2-20000000000002i−2i00000000000000000000000000000000
χ6944-4-4-2−4i4i4i−4i-4422-244-4-40000−4i4i00002i−2i−2i2i2-2-2-2220000000000002i−2i00000000000000000000000000000000
χ7044-4-4-2−4i4i4i−4i-4422-2-4-44400004i−4i00002i−2i−2i2i2-222-2-2000000000000−2i2i00000000000000000000000000000000
χ7144-4-4-2−4i4i−4i4i4-422-200000000004i−4i-442i−2i2i−2i-22000000000000000000−2i2i2-20000000000000000000000000000
χ7244-4-4-2−4i4i−4i4i4-422-20000000000−4i4i4-42i−2i2i−2i-220000000000000000002i−2i-220000000000000000000000000000
χ734-44-440000004-4-422−2222−22000000000000000022−2222−22−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ4300000000000000000000000000000000000000
χ744-44-440000004-4-422−2222−22000000000000000022−2222−222ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4300000000000000000000000000000000000000
χ754-44-440000004-4-4−2222−22220000000000000000−2222−22222ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ4700000000000000000000000000000000000000
χ764-44-440000004-4-4−2222−22220000000000000000−2222−2222−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ4700000000000000000000000000000000000000
χ774-4-444000000-44-422−22−2222000000000000000022−22−22222ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ4700000000000000000000000000000000000000
χ784-4-444000000-44-422−22−2222000000000000000022−22−2222−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ4700000000000000000000000000000000000000
χ794-4-444000000-44-4−222222−220000000000000000−222222−22−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ4300000000000000000000000000000000000000
χ804-4-444000000-44-4−222222−220000000000000000−222222−222ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4300000000000000000000000000000000000000
χ818-88-8-4000000-44442−4242−420000000000000000−2222−22220000000000000000000000000000000000000000000000
χ828-88-8-4000000-444−4242−4242000000000000000022−2222−220000000000000000000000000000000000000000000000
χ838-8-88-40000004-4442−42−42420000000000000000−222222−220000000000000000000000000000000000000000000000
χ848-8-88-40000004-44−424242−42000000000000000022−22−22220000000000000000000000000000000000000000000000

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