Finite Group Databasebeta

← Group #10713256

Character table — Group #10713256

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order12442223444688881212666881212121616161616161616242424241616161616161616242448484848484848484444888816161616888824242424242424248888
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
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ911-1-11-1-11-1111-1-111-1-11-1-11-1-111iiii−i−i−i−i11-1-11111-1-1-1-11-1iiii−i−i−i−iii−i−iii−i−i11-1-1i−i1-1ii−i−i11-1-1i−i1-1
χ1011-1-11-1-11-1111-1-111-1-11-1-11-1-111iiii−i−i−i−i11-1-11111-1-1-1-11-1iiii−i−i−i−iii−i−iii−i−i11-1-1−ii-11−i−iii-1-111−ii-11
χ1111-1-11-1-11-1111-1-111-1-11-1-11-1-111iiii−i−i−i−i11-1-1-1-1-1-111111-1iiii−i−i−i−i−i−iii−i−iii-1-111i−i1-1ii−i−i11-1-1−ii-11
χ1211-1-11-1-11-1111-1-111-1-11-1-11-1-111iiii−i−i−i−i11-1-1-1-1-1-111111-1iiii−i−i−i−i−i−iii−i−iii-1-111−ii-11−i−iii-1-111i−i1-1
χ1311-1-11-1-11-1111-1-111-1-11-1-11-1-111−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−i−i−iiiii−i−iii−i−iii11-1-1i−i-11ii−i−i-1-111i−i-11
χ1411-1-11-1-11-1111-1-111-1-11-1-11-1-111−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−i−i−iiiii−i−iii−i−iii11-1-1−ii1-1−i−iii11-1-1−ii1-1
χ1511-1-11-1-11-1111-1-111-1-11-1-11-1-111−i−i−i−iiiii11-1-1-1-1-1-111111-1−i−i−i−iiiiiii−i−iii−i−i-1-111i−i-11ii−i−i-1-111−ii1-1
χ1611-1-11-1-11-1111-1-111-1-11-1-11-1-111−i−i−i−iiiii11-1-1-1-1-1-111111-1−i−i−i−iiiiiii−i−iii−i−i-1-111−ii1-1−i−iii11-1-1i−i-11
χ17222222222222-2-2-2-222222-2-222200000000-2-2-2-200000000-2-2000000002222-2-2-2-200000000000000000000
χ18222222222222-2-2-2-222222-2-222200000000-2-2-2-200000000-2-200000000-2-2-2-2222200000000000000000000
χ192222222-1222-12222-1-1-1-1-122-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ202222222-1222-12222-1-1-1-1-122-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ212222222-1222-12222-1-1-1-1-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ222222222-1222-12222-1-1-1-1-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ2322222-2-222-2-220000222-2-2002-2-2−i2−i2i2i2−i2−i2i2i2000022−2−222−2−200−i2−i2i2i2−i2−i2i2i22i−2i2i−2i00002−22−20000000000000000
χ2422222-2-222-2-220000222-2-2002-2-2−i2−i2i2i2−i2−i2i2i20000−2−222−2−22200−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i0000−22−220000000000000000
χ2522222-2-222-2-220000222-2-2002-2-2i2i2−i2−i2i2i2−i2−i2000022−2−222−2−200i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i00002−22−20000000000000000
χ2622222-2-222-2-220000222-2-2002-2-2i2i2−i2−i2i2i2−i2−i20000−2−222−2−22200i2i2−i2−i2i2i2−i2−i22i−2i2i−2i0000−22−220000000000000000
χ272222-22-22-2-222000022-22-200-2-222−22−22−22−2000022−2−222−2−2002−22−22−22−200002-22-2−22−220000000000000000
χ282222-22-22-2-222000022-22-200-2-222−22−22−22−20000−2−222−2−222002−22−22−22−20000-22-222−22−20000000000000000
χ292222-22-22-2-222000022-22-200-2-22−22−22−22−22000022−2−222−2−200−22−22−22−220000-22-22−22−220000000000000000
χ302222-22-22-2-222000022-22-200-2-22−22−22−22−220000−2−222−2−22200−22−22−22−2200002-22-22−22−20000000000000000
χ312222-2-222-22-22222222-2-22-2-2-22-200000000222222222222-2-20000000000000000-2-2-2-20000000000000000
χ322222-2-222-22-22222222-2-22-2-2-22-2000000002222-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ332222-2-222-22-22-2-2-2-222-2-2222-22-22i−2i−2i2i2i−2i−2i2i-2-2-2-200000000222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ342222-2-222-22-22-2-2-2-222-2-2222-22-2−2i2i2i−2i−2i2i2i−2i-2-2-2-20000000022−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ352222-2-22-1-22-2-1-2-2-2-2-1-111-1221-112i−2i−2i2i2i−2i−2i2i111100000000-1-1−iii−i−iii−i0000000000000000−i3i3−i3i33−33−30000
χ362222-2-22-1-22-2-1-2-2-2-2-1-111-1221-112i−2i−2i2i2i−2i−2i2i111100000000-1-1−iii−i−iii−i0000000000000000i3−i3i3−i3−33−330000
χ372222-2-22-1-22-2-1-2-2-2-2-1-111-1221-11−2i2i2i−2i−2i2i2i−2i111100000000-1-1i−i−iii−i−ii0000000000000000−i3i3−i3i3−33−330000
χ382222-2-22-1-22-2-1-2-2-2-2-1-111-1221-11−2i2i2i−2i−2i2i2i−2i111100000000-1-1i−i−iii−i−ii0000000000000000i3−i3i3−i33−33−30000
χ3922-2-22222-2-2-220000-2-222200-2-2-222−2−2−2−222000022−2−2−2−2220022−2−2−2−222-222-200002−2−220000000000000000
χ4022-2-22222-2-2-220000-2-222200-2-2-222−2−2−2−2220000−2−22222−2−20022−2−2−2−2222-2-220000−222−20000000000000000
χ4122-2-22222-2-2-220000-2-222200-2-2-2−2−22222−2−2000022−2−2−2−22200−2−22222−2−22-2-2200002−2−220000000000000000
χ4222-2-22222-2-2-220000-2-222200-2-2-2−2−22222−2−20000−2−22222−2−200−2−22222−2−2-222-20000−222−20000000000000000
χ4322-2-22-2-22-222222-2-2-2-22-2-2-22-22200000000-2-22200000000-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4422-2-22-2-22-222222-2-2-2-22-2-2-22-22200000000-2-22200000000-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4522-2-22-2-2-1-222-1-2-22211-1112-21-1-12i2i2i2i−2i−2i−2i−2i-1-11100000000-11−i−i−i−iiiii0000000000002i−2i2-2−i−iii-1-1110000
χ4622-2-22-2-2-1-222-1-2-22211-1112-21-1-12i2i2i2i−2i−2i−2i−2i-1-11100000000-11−i−i−i−iiiii000000000000−2i2i-22ii−i−i11-1-10000
χ4722-2-22-2-2-1-222-1-2-22211-1112-21-1-1−2i−2i−2i−2i2i2i2i2i-1-11100000000-11iiii−i−i−i−i0000000000002i−2i-22−i−iii11-1-10000
χ4822-2-22-2-2-1-222-1-2-22211-1112-21-1-1−2i−2i−2i−2i2i2i2i2i-1-11100000000-11iiii−i−i−i−i000000000000−2i2i2-2ii−i−i-1-1110000
χ4922-2-2-22-2222-2222-2-2-2-2-22-22-222-22-2-22-222-2-2-222000000002-22-2-22-222-20000000000000000000000000000
χ5022-2-2-22-2222-2222-2-2-2-2-22-22-222-2-222-22-2-22-2-222000000002-2-222-22-2-220000000000000000000000000000
χ5122-2-2-22-2222-22-2-222-2-2-22-2-2222-20000000022-2-22222-2-2-2-2-220000000000000000-2-2220000000000000000
χ5222-2-2-22-2222-22-2-222-2-2-22-2-2222-20000000022-2-2-2-2-2-22222-22000000000000000022-2-20000000000000000
χ5322-2-2-22-2-122-2-122-2-2111-112-2-1-112-2-22-222-211-1-100000000-11-111-11-1-1100000000000000003−3−33−333−30000
χ5422-2-2-22-2-122-2-122-2-2111-112-2-1-112-2-22-222-211-1-100000000-11-111-11-1-110000000000000000−333−33−3−330000
χ5522-2-2-22-2-122-2-122-2-2111-112-2-1-11-222-22-2-2211-1-100000000-111-1-11-111-100000000000000003−3−333−3−330000
χ5622-2-2-22-2-122-2-122-2-2111-112-2-1-11-222-22-2-2211-1-100000000-111-1-11-111-10000000000000000−333−3−333−30000
χ5722-2-2-2-2222-2220000-2-2-2-22002-22−i2i2−i2i2i2−i2i2−i2000022−2−2−2−22200−i2i2−i2i2i2−i2i2−i20000−2i2i2i−2i−222−20000000000000000
χ5822-2-2-2-2222-2220000-2-2-2-22002-22−i2i2−i2i2i2−i2i2−i20000−2−22222−2−200−i2i2−i2i2i2−i2i2−i200002i−2i−2i2i2−2−220000000000000000
χ5922-2-2-2-2222-2220000-2-2-2-22002-22i2−i2i2−i2−i2i2−i2i2000022−2−2−2−22200i2−i2i2−i2−i2i2−i2i200002i−2i−2i2i−222−20000000000000000
χ6022-2-2-2-2222-2220000-2-2-2-22002-22i2−i2i2−i2−i2i2−i2i20000−2−22222−2−200i2−i2i2−i2−i2i2−i2i20000−2i2i2i−2i2−2−220000000000000000
χ614444444-2444-2-4-4-4-4-2-2-2-2-2-4-4-2-2-20000000022220000000022000000000000000000000000000000000000
χ6244444-4-4-24-4-4-20000-2-2-22200-222−2i2−2i22i22i2−2i2−2i22i22i200000000000000i2i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ6344444-4-4-24-4-4-20000-2-2-22200-2222i22i2−2i2−2i22i22i2−2i2−2i200000000000000−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ644444-44-4-2-4-44-20000-2-22-220022-222−2222−2222−2222−2200000000000000−22−22−22−220000000000000000000000000000
χ654444-44-4-2-4-44-20000-2-22-220022-2−2222−2222−2222−2222000000000000002−22−22−22−20000000000000000000000000000
χ664444-4-44-2-44-4-24444-2-222-2-4-42-2200000000-2-2-2-20000000022000000000000000000000000000000000000
χ6744-4-4444-2-4-4-4-2000022-2-2-2002222222−22−22−22−22222200000000000000−2−22222−2−20000000000000000000000000000
χ6844-4-4444-2-4-4-4-2000022-2-2-200222−22−2222222222−22−220000000000000022−2−2−2−2220000000000000000000000000000
χ6944-4-44-4-4-2-444-244-4-422-222-442-2-20000000022-2-2000000002-2000000000000000000000000000000000000
χ7044-4-4-44-4-244-4-2-4-444222-22-44-2-2200000000-2-222000000002-2000000000000000000000000000000000000
χ7144-4-4-4-44-24-44-200002222-200-22-2−2i22i2−2i22i22i2−2i22i2−2i200000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ7244-4-4-4-44-24-44-200002222-200-22-22i2−2i22i2−2i2−2i22i2−2i22i200000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ734-44i−4i0004000-4−2i22i222−224i−4i000000000000000022−22−2i22i2−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000000000000000000000000000000000
χ744-44i−4i0004000-4−2i22i222−224i−4i000000000000000022−22−2i22i22ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000000000000000000000000000000000
χ754-44i−4i0004000-42i2−2i2−22224i−4i0000000000000000−22222i2−2i22ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000000000000000000000000000000
χ764-44i−4i0004000-42i2−2i2−22224i−4i0000000000000000−22222i2−2i2−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000000000000000000000000000000
χ774-4−4i4i0004000-4−2i22i2−2222−4i4i0000000000000000−2222−2i22i22ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000000000000000000000000000000
χ784-4−4i4i0004000-4−2i22i2−2222−4i4i0000000000000000−2222−2i22i2−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000000000000000000000000000000
χ794-4−4i4i0004000-42i2−2i222−22−4i4i000000000000000022−222i2−2i2−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000000000000000000000000000000000
χ804-4−4i4i0004000-42i2−2i222−22−4i4i000000000000000022−222i2−2i22ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000000000000000000000000000000000
χ818-88i−8i000-40004−4i24i242−42−4i4i0000000000000000−22222i2−2i20000000000000000000000000000000000000000000000
χ828-88i−8i000-400044i2−4i2−4242−4i4i000000000000000022−22−2i22i20000000000000000000000000000000000000000000000
χ838-8−8i8i000-40004−4i24i2−42424i−4i000000000000000022−222i2−2i20000000000000000000000000000000000000000000000
χ848-8−8i8i000-400044i2−4i242−424i−4i0000000000000000−2222−2i22i20000000000000000000000000000000000000000000000

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