Finite Group Databasebeta

← Group #10713613

Character table — Group #10713613

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order1222223444466688886688121212121616161616161616242424241616161616161616242448484848484848484444888816161616448812121212242424242288
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
χ91-1-111-1111-1-1-1-11-1-1111-11-11-11-1iiii−i−i−i−i11-1-11111-1-1-1-11-1iiii−i−i−i−iii−i−iii−i−i11-1-11-1i−i11-1-1ii−i−i1-1i−i
χ101-1-111-1111-1-1-1-11-1-1111-11-11-11-1iiii−i−i−i−i11-1-11111-1-1-1-11-1iiii−i−i−i−iii−i−iii−i−i11-1-1-11−ii-1-111−i−iii-11−ii
χ111-1-111-1111-1-1-1-11-1-1111-11-11-11-1iiii−i−i−i−i11-1-1-1-1-1-111111-1iiii−i−i−i−i−i−iii−i−iii-1-1111-1i−i11-1-1ii−i−i-11−ii
χ121-1-111-1111-1-1-1-11-1-1111-11-11-11-1iiii−i−i−i−i11-1-1-1-1-1-111111-1iiii−i−i−i−i−i−iii−i−iii-1-111-11−ii-1-111−i−iii1-1i−i
χ131-1-111-1111-1-1-1-11-1-1111-11-11-11-1−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−i−i−iiiii−i−iii−i−iii11-1-11-1−ii11-1-1−i−iii1-1−ii
χ141-1-111-1111-1-1-1-11-1-1111-11-11-11-1−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−i−i−iiiii−i−iii−i−iii11-1-1-11i−i-1-111ii−i−i-11i−i
χ151-1-111-1111-1-1-1-11-1-1111-11-11-11-1−i−i−i−iiiii11-1-1-1-1-1-111111-1−i−i−i−iiiiiii−i−iii−i−i-1-1111-1−ii11-1-1−i−iii-11i−i
χ161-1-111-1111-1-1-1-11-1-1111-11-11-11-1−i−i−i−iiiii11-1-1-1-1-1-111111-1−i−i−i−iiiiiii−i−iii−i−i-1-111-11i−i-1-111ii−i−i1-1−ii
χ1722222222222222-2-2-2-222-2-2222200000000-2-2-2-200000000-2-2000000002222-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-222-2-2222200000000-2-2-2-200000000-2-200000000-2-2-2-2222200000000000000000000
χ192222222-2-2-2-222200002200-2-2-2-2−i2−i2i2i2−i2−i2i2i2000022−2−222−2−200−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i2−22−20000000000000000
χ202222222-2-2-2-222200002200-2-2-2-2−i2−i2i2i2−i2−i2i2i20000−2−222−2−22200−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i−22−220000000000000000
χ212222222-2-2-2-222200002200-2-2-2-2i2i2−i2−i2i2i2−i2−i2000022−2−222−2−200i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i2−22−20000000000000000
χ222222222-2-2-2-222200002200-2-2-2-2i2i2−i2−i2i2i2−i2−i20000−2−222−2−22200i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i−22−220000000000000000
χ23222222-12222-1-1-12222-1-122-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ24222222-12222-1-1-12222-1-122-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ25222222-12222-1-1-12222-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ26222222-12222-1-1-12222-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ272222-2-222-2-222220000-2-2002-2-222−22−22−22−2000022−2−222−2−2002−22−22−22−22-22-20000−22−220000000000000000
χ282222-2-222-2-222220000-2-2002-2-222−22−22−22−20000−2−222−2−222002−22−22−22−2-22-2200002−22−20000000000000000
χ292222-2-222-2-222220000-2-2002-2-22−22−22−22−22000022−2−222−2−200−22−22−22−22-22-220000−22−220000000000000000
χ302222-2-222-2-222220000-2-2002-2-22−22−22−22−220000−2−222−2−22200−22−22−22−222-22-200002−22−20000000000000000
χ312222-2-22-222-22222222-2-2-2-2-222-200000000222222222222-2-20000000000000000-2-2-2-20000000000000000
χ322222-2-22-222-22222222-2-2-2-2-222-2000000002222-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ332222-2-22-222-2222-2-2-2-2-2-222-222-22i−2i−2i2i2i−2i−2i2i-2-2-2-200000000222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ342222-2-22-222-2222-2-2-2-2-2-222-222-2−2i2i2i−2i−2i2i2i−2i-2-2-2-20000000022−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ352222-2-2-1-222-2-1-1-1-2-2-2-211221-1-112i−2i−2i2i2i−2i−2i2i111100000000-1-1−iii−i−iii−i0000000000000000−i3i3−i3i33−33−30000
χ362222-2-2-1-222-2-1-1-1-2-2-2-211221-1-112i−2i−2i2i2i−2i−2i2i111100000000-1-1−iii−i−iii−i0000000000000000i3−i3i3−i3−33−330000
χ372222-2-2-1-222-2-1-1-1-2-2-2-211221-1-11−2i2i2i−2i−2i2i2i−2i111100000000-1-1i−i−iii−i−ii0000000000000000−i3i3−i3i3−33−330000
χ382222-2-2-1-222-2-1-1-1-2-2-2-211221-1-11−2i2i2i−2i−2i2i2i−2i111100000000-1-1i−i−iii−i−ii0000000000000000i3−i3i3−i33−33−30000
χ392-2-222-2222-2-2-2-2222-2-22-2-222-22-200000000-2-22200000000-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ402-2-222-2222-2-2-2-2222-2-22-2-222-22-200000000-2-22200000000-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ412-2-222-22-2-222-2-2200002-200-22-2222−2−2−2−222000022−2−2−2−2220022−2−2−2−2220000-222-22−2−220000000000000000
χ422-2-222-22-2-222-2-2200002-200-22-2222−2−2−2−2220000−2−22222−2−20022−2−2−2−22200002-2-22−222−20000000000000000
χ432-2-222-22-2-222-2-2200002-200-22-22−2−22222−2−2000022−2−2−2−22200−2−22222−2−200002-2-222−2−220000000000000000
χ442-2-222-22-2-222-2-2200002-200-22-22−2−22222−2−20000−2−22222−2−200−2−22222−2−20000-222-2−222−20000000000000000
χ452-2-222-2-122-2-211-1-2-222-112-2-11-112i2i2i2i−2i−2i−2i−2i-1-11100000000-11−i−i−i−iiiii0000000000002-22i−2i-1-111−i−iii0000
χ462-2-222-2-122-2-211-1-2-222-112-2-11-112i2i2i2i−2i−2i−2i−2i-1-11100000000-11−i−i−i−iiiii000000000000-22−2i2i11-1-1ii−i−i0000
χ472-2-222-2-122-2-211-1-2-222-112-2-11-11−2i−2i−2i−2i2i2i2i2i-1-11100000000-11iiii−i−i−i−i0000000000002-2−2i2i-1-111ii−i−i0000
χ482-2-222-2-122-2-211-1-2-222-112-2-11-11−2i−2i−2i−2i2i2i2i2i-1-11100000000-11iiii−i−i−i−i000000000000-222i−2i11-1-1−i−iii0000
χ492-2-22-2222-22-2-2-220000-220022-2-2−i2i2−i2i2i2−i2i2−i2000022−2−2−2−22200−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i0000−222−20000000000000000
χ502-2-22-2222-22-2-2-220000-220022-2-2−i2i2−i2i2i2−i2i2−i20000−2−22222−2−200−i2i2−i2i2i2−i2i2−i22i−2i−2i2i00002−2−220000000000000000
χ512-2-22-2222-22-2-2-220000-220022-2-2i2−i2i2−i2−i2i2−i2i2000022−2−2−2−22200i2−i2i2−i2−i2i2−i2i22i−2i−2i2i0000−222−20000000000000000
χ522-2-22-2222-22-2-2-220000-220022-2-2i2−i2i2−i2−i2i2−i2i20000−2−22222−2−200i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i00002−2−220000000000000000
χ532-2-22-222-22-22-2-2222-2-2-222-2-2-2222-2-22-222-2-2-222000000002-22-2-22-222-20000000000000000000000000000
χ542-2-22-222-22-22-2-2222-2-2-222-2-2-222-222-22-2-22-2-222000000002-2-222-22-2-220000000000000000000000000000
χ552-2-22-222-22-22-2-22-2-222-22-22-2-2220000000022-2-22222-2-2-2-2-220000000000000000-2-2220000000000000000
χ562-2-22-222-22-22-2-22-2-222-22-22-2-2220000000022-2-2-2-2-2-22222-22000000000000000022-2-20000000000000000
χ572-2-22-22-1-22-2211-122-2-21-12-211-1-12-2-22-222-211-1-100000000-11-111-11-1-110000000000000000−i3i3i3−i3−i3i3i3−i30000
χ582-2-22-22-1-22-2211-122-2-21-12-211-1-12-2-22-222-211-1-100000000-11-111-11-1-110000000000000000i3−i3−i3i3i3−i3−i3i30000
χ592-2-22-22-1-22-2211-122-2-21-12-211-1-1-222-22-2-2211-1-100000000-111-1-11-111-10000000000000000−i3i3i3−i3i3−i3−i3i30000
χ602-2-22-22-1-22-2211-122-2-21-12-211-1-1-222-22-2-2211-1-100000000-111-1-11-111-10000000000000000i3−i3−i3i3−i3i3i3−i30000
χ61444444-24444-2-2-2-4-4-4-4-2-2-4-4-2-2-2-20000000022220000000022000000000000000000000000000000000000
χ62444444-2-4-4-4-4-2-2-20000-2-2002222−2i2−2i22i22i2−2i2−2i22i22i200000000000000i2i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ63444444-2-4-4-4-4-2-2-20000-2-20022222i22i2−2i2−2i22i22i2−2i2−2i200000000000000−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ644444-4-4-24-4-44-2-2-200002200-222-222−2222−2222−2222−2200000000000000−22−22−22−220000000000000000000000000000
χ654444-4-4-24-4-44-2-2-200002200-222-2−2222−2222−2222−2222000000000000002−22−22−22−20000000000000000000000000000
χ664444-4-4-2-444-4-2-2-2444422-4-42-2-2200000000-2-2-2-20000000022000000000000000000000000000000000000
χ6744-4-400400004-4-422−2222−22000000000000000022−2222−22−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ4300000000000000000000000000000000000000
χ6844-4-400400004-4-422−2222−22000000000000000022−2222−222ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4300000000000000000000000000000000000000
χ6944-4-400400004-4-4−2222−22220000000000000000−2222−22222ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ4700000000000000000000000000000000000000
χ7044-4-400400004-4-4−2222−22220000000000000000−2222−2222−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ4700000000000000000000000000000000000000
χ714-44-40040000-44-422−22−22220000000000000000−222222−222ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ4700000000000000000000000000000000000000
χ724-44-40040000-44-422−22−22220000000000000000−222222−22−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ4700000000000000000000000000000000000000
χ734-44-40040000-44-4−222222−22000000000000000022−22−2222−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4300000000000000000000000000000000000000
χ744-44-40040000-44-4−222222−22000000000000000022−22−22222ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ4300000000000000000000000000000000000000
χ754-4-444-4-244-4-422-244-4-4-22-44-22-220000000022-2-2000000002-2000000000000000000000000000000000000
χ764-4-444-4-2-4-44422-20000-22002-22-22222−22−22−22−22222200000000000000−2−22222−2−20000000000000000000000000000
χ774-4-444-4-2-4-44422-20000-22002-22-2−22−2222222222−22−220000000000000022−2−2−2−2220000000000000000000000000000
χ784-4-44-44-24-44-422-200002-200-2-222−2i22i2−2i22i22i2−2i22i2−2i200000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ794-4-44-44-24-44-422-200002-200-2-2222i2−2i22i2−2i2−2i22i2−2i22i200000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ804-4-44-44-2-44-4422-2-4-4442-2-4422-2-200000000-2-222000000002-2000000000000000000000000000000000000
χ8188-8-800-40000-44442−4242−420000000000000000−2222−22220000000000000000000000000000000000000000000000
χ8288-8-800-40000-444−4242−4242000000000000000022−2222−220000000000000000000000000000000000000000000000
χ838-88-800-400004-4442−42−4242000000000000000022−22−22220000000000000000000000000000000000000000000000
χ848-88-800-400004-44−424242−420000000000000000−222222−220000000000000000000000000000000000000000000000

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