Finite Group Databasebeta

← Group #10713600

Character table — Group #10713600

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order124422234446888812124444666888888121212242424241616161616161616121212122424242424241616161616161616161616162444661212121212122444
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
χ5111111111111111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ911-1-11-1-111-11111-1-1-1-1ii−i−i1-1-1ii−i−i1-11-1111-1-11111-1-1-1-1ii−i−iii−i−i1-111-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ1011-1-11-1-111-11111-1-1-1-1ii−i−i1-1-1ii−i−i1-11-1111-1-11111-1-1-1-1ii−i−iii−i−i1-111-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ1111-1-11-1-111-11111-1-1-1-1ii−i−i1-1-1ii−i−i1-11-1111-1-1-1-1-1-11111ii−i−iii−i−i1-1-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ1211-1-11-1-111-11111-1-1-1-1ii−i−i1-1-1ii−i−i1-11-1111-1-1-1-1-1-11111ii−i−iii−i−i1-1-1-111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ1311-1-11-1-111-11111-1-1-1-1−i−iii1-1-1−i−iii1-11-1111-1-11111-1-1-1-1−i−iii−i−iii1-111-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ1411-1-11-1-111-11111-1-1-1-1−i−iii1-1-1−i−iii1-11-1111-1-11111-1-1-1-1−i−iii−i−iii1-111-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ1511-1-11-1-111-11111-1-1-1-1−i−iii1-1-1−i−iii1-11-1111-1-1-1-1-1-11111−i−iii−i−iii1-1-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ1611-1-11-1-111-11111-1-1-1-1−i−iii1-1-1−i−iii1-11-1111-1-1-1-1-1-11111−i−iii−i−iii1-1-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ17222222222222-2-2-2-2222222222-2-2-2-2-2-2222-2-2-2-2000000002222-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-22222222-2-2222-2-2-2-200000000-2-2-2-22222-2-20000000000000000000000000000
χ192222222-1222-12222-1-12222-1-1-1222222-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ202222222-1222-12222-1-12222-1-1-1222222-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ212222222-1222-12222-1-1-2-2-2-2-1-1-1-2-2-2-222-1-1-1-1-1-1-10000000011111111-1-100000000000022-2-2-1-1-1-111110000
χ222222222-1222-12222-1-1-2-2-2-2-1-1-1-2-2-2-222-1-1-1-1-1-1-10000000011111111-1-1000000000000-2-2221111-1-1-1-10000
χ232222222-1222-1-2-2-2-2-1-12222-1-1-1-2-2-2-2-2-2-1-1-1111100000000-1-1-1-11111110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ242222222-1222-1-2-2-2-2-1-12222-1-1-1-2-2-2-2-2-2-1-1-1111100000000-1-1-1-11111110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ252222222-1222-1-2-2-2-2-1-1-2-2-2-2-1-1-12222-2-2-1-1-11111000000001111-1-1-1-1110000000000000000−i3i3−i3i3i3−i3i3−i30000
χ262222222-1222-1-2-2-2-2-1-1-2-2-2-2-1-1-12222-2-2-1-1-11111000000001111-1-1-1-1110000000000000000i3−i3i3−i3−i3i3−i3i30000
χ2722222-2-22-22-220000222i−2i2i−2i2-2-2000000-22-2000022−2−222−2−22i−2i2i−2i0000002−22−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ2822222-2-22-22-220000222i−2i2i−2i2-2-2000000-22-20000−2−222−2−2222i−2i2i−2i000000−22−22i2i2−i2−i2i2i2−i2−i20000000000000000
χ2922222-2-22-22-22000022−2i2i−2i2i2-2-2000000-22-2000022−2−222−2−2−2i2i−2i2i0000002−22−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3022222-2-22-22-22000022−2i2i−2i2i2-2-2000000-22-20000−2−222−2−222−2i2i−2i2i000000−22−22−i2−i2i2i2−i2−i2i2i20000000000000000
χ312222-22-22-2-2222222220000-22-20000-2-2-2-2222222222222200000000-2-2-2-2-2-2000000000000000000000000
χ322222-22-22-2-2222222220000-22-20000-2-2-2-222222-2-2-2-2-2-2-2-200000000-2-22222000000000000000000000000
χ332222-22-22-2-222-2-2-2-2220000-22-2000022-2-22-2-2-2-200000000000000002200002i−2i2i−2i2i−2i2i−2i0000000000000000
χ342222-22-22-2-222-2-2-2-2220000-22-2000022-2-22-2-2-2-20000000000000000220000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ352222-2-2222-2-220000220000-2-222-22-2002-2-2000022−2−222−2−200002-22-200−22−222−2−222−2−220000000000000000
χ362222-2-2222-2-220000220000-2-222-22-2002-2-20000−2−222−2−22200002-22-2002−22−2−222−2−222−20000000000000000
χ372222-2-2222-2-220000220000-2-22-22-22002-2-2000022−2−222−2−20000-22-2200−22−22−222−2−222−20000000000000000
χ382222-2-2222-2-220000220000-2-22-22-22002-2-20000−2−222−2−2220000-22-22002−22−22−2−222−2−220000000000000000
χ3922-2-22222-2-2-220000-2-22-2-22222000000-2-2-2000022−2−2−2−2222-2-220000002−2−22−2−22222−2−20000000000000000
χ4022-2-22222-2-2-220000-2-22-2-22222000000-2-2-20000−2−22222−2−22-2-22000000−222−222−2−2−2−2220000000000000000
χ4122-2-22222-2-2-220000-2-2-222-2222000000-2-2-2000022−2−2−2−222-222-20000002−2−2222−2−2−2−2220000000000000000
χ4222-2-22222-2-2-220000-2-2-222-2222000000-2-2-20000−2−22222−2−2-222-2000000−222−2−2−22222−2−20000000000000000
χ4322-2-22-2-222-222-2-222-2-22i2i−2i−2i2-2-2−2i−2i2i2i-222-22-2-222000000002i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000
χ4422-2-22-2-222-222-2-222-2-2−2i−2i2i2i2-2-22i2i−2i−2i-222-22-2-22200000000−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000
χ4522-2-22-2-2-12-22-122-2-2112i2i−2i−2i-1112i2i−2i−2i2-2-11-1-1-11100000000−i−iii−i−iii-110000000000002-22i−2i-1-111−i−iii0000
χ4622-2-22-2-2-12-22-122-2-2112i2i−2i−2i-1112i2i−2i−2i2-2-11-1-1-11100000000−i−iii−i−iii-11000000000000-22−2i2i11-1-1ii−i−i0000
χ4722-2-22-2-2-12-22-122-2-211−2i−2i2i2i-111−2i−2i2i2i2-2-11-1-1-11100000000ii−i−iii−i−i-110000000000002-2−2i2i-1-111ii−i−i0000
χ4822-2-22-2-2-12-22-122-2-211−2i−2i2i2i-111−2i−2i2i2i2-2-11-1-1-11100000000ii−i−iii−i−i-11000000000000-222i−2i11-1-1−i−iii0000
χ4922-2-22-2-2-12-22-1-2-222112i2i−2i−2i-111−2i−2i2i2i-22-11-111-1-100000000−i−iiiii−i−i1-10000000000000000−i3i3i3−i33−3−330000
χ5022-2-22-2-2-12-22-1-2-222112i2i−2i−2i-111−2i−2i2i2i-22-11-111-1-100000000−i−iiiii−i−i1-10000000000000000i3−i3−i3i3−333−30000
χ5122-2-22-2-2-12-22-1-2-22211−2i−2i2i2i-1112i2i−2i−2i-22-11-111-1-100000000ii−i−i−i−iii1-10000000000000000−i3i3i3−i3−333−30000
χ5222-2-22-2-2-12-22-1-2-22211−2i−2i2i2i-1112i2i−2i−2i-22-11-111-1-100000000ii−i−i−i−iii1-10000000000000000i3−i3−i3i33−3−330000
χ5322-2-2-22-2222-220000-2-20000-22-22i−2i−2i2i0022-2000022−2−2−2−22200002i−2i−2i2i00−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5422-2-2-22-2222-220000-2-20000-22-22i−2i−2i2i0022-20000−2−22222−2−200002i−2i−2i2i002−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ5522-2-2-22-2222-220000-2-20000-22-2−2i2i2i−2i0022-2000022−2−2−2−2220000−2i2i2i−2i00−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5622-2-2-22-2222-220000-2-20000-22-2−2i2i2i−2i0022-20000−2−22222−2−20000−2i2i2i−2i002−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ5722-2-2-2-222-222222-2-2-2-20000-2-220000-22-22222-2-22222-2-2-2-200000000-22-2-222000000000000000000000000
χ5822-2-2-2-222-222222-2-2-2-20000-2-220000-22-22222-2-2-2-2-2-2222200000000-2222-2-2000000000000000000000000
χ5922-2-2-2-222-2222-2-222-2-20000-2-2200002-2-222-2-22200000000000000002-200002-22-2-22-220000000000000000
χ6022-2-2-2-222-2222-2-222-2-20000-2-2200002-2-222-2-22200000000000000002-20000-22-222-22-20000000000000000
χ6144444-4-4-2-44-4-20000-2-24i−4i4i−4i-2220000002-22000000000000−2i2i−2i2i0000000000000000000000000000000000
χ6244444-4-4-2-44-4-20000-2-2−4i4i−4i4i-2220000002-220000000000002i−2i2i−2i0000000000000000000000000000000000
χ634444-44-4-2-4-44-24444-2-200002-220000-4-422-2-2-2-2-20000000000000000220000000000000000000000000000
χ644444-44-4-2-4-44-2-4-4-4-4-2-200002-2200004422-222220000000000000000-2-20000000000000000000000000000
χ654444-4-44-24-4-4-20000-2-2000022-24-44-400-2220000000000000000-22-22000000000000000000000000000000
χ664444-4-44-24-4-4-20000-2-2000022-2-44-4400-22200000000000000002-22-2000000000000000000000000000000
χ6744-4-4444-2-4-4-4-20000224-4-44-2-2-2000000222000000000000-222-20000000000000000000000000000000000
χ6844-4-4444-2-4-4-4-2000022-444-4-2-2-20000002220000000000002-2-220000000000000000000000000000000000
χ6944-4-4-44-4-244-4-200002200002-224i−4i−4i4i00-2-220000000000000000−2i2i2i−2i000000000000000000000000000000
χ7044-4-4-44-4-244-4-200002200002-22−4i4i4i−4i00-2-2200000000000000002i−2i−2i2i000000000000000000000000000000
χ7144-4-4-4-44-2-444-244-4-422000022-20000-442-2-2-2-22200000000000000002-20000000000000000000000000000
χ7244-4-4-4-44-2-444-2-4-44422000022-200004-42-2-222-2-20000000000000000-220000000000000000000000000000
χ734-44i−4i0004000-422−22−2i22i24i−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−4i0004000-422−22−2i22i24i−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−4i0004000-4−22222i2−2i24i−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−4i0004000-4−22222i2−2i24i−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
χ774-4−4i4i0004000-422−222i2−2i2−4i4i000000000000000022−222i2−2i2−2ζ25+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
χ784-4−4i4i0004000-422−222i2−2i2−4i4i000000000000000022−222i2−2i22ζ25−2ζ31+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
χ794-4−4i4i0004000-4−2222−2i22i2−4i4i0000000000000000−2222−2i22i22ζ11−2ζ13−2ζ29+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
χ804-4−4i4i0004000-4−2222−2i22i2−4i4i0000000000000000−2222−2i22i2−2ζ11+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
χ818-88i−8i000-4000442−42−4i24i2−4i4i0000000000000000−22222i2−2i20000000000000000000000000000000000000000000000
χ828-88i−8i000-40004−42424i2−4i2−4i4i000000000000000022−22−2i22i20000000000000000000000000000000000000000000000
χ838-8−8i8i000-4000442−424i2−4i24i−4i0000000000000000−2222−2i22i20000000000000000000000000000000000000000000000
χ848-8−8i8i000-40004−4242−4i24i24i−4i000000000000000022−222i2−2i20000000000000000000000000000000000000000000000

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