Finite Group Databasebeta

← Group #10951663

Character table — Group #10951663

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444446688888888888888881212121212121212121616161616161624242424243232484848
order122234466688882412121212161616162424242422446816162424484848484848484844488161616162246612122281616612244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1
χ31111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111
χ511111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111111-1-1-1-11-1-11111-1-11-1-1-1-1-111
χ611111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-1-1-1111-1-1111-1-1
χ711111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-111-1-11-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-11111-111
χ911111111111111-1-11-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-11-1-1-11111-1-1-11-1-1-11
χ1011111111111111-1-11-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1111-1-1-1-1-1-1-1-1111-1
χ1111111111111111-1-11-1-1111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-11111-111-1
χ1211111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11-1111-1-111111-11-1-11
χ1311111111111111-1-11-1-11-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-1-1-11-1-111-1-1-111-111-11
χ1411111111111111-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1-1-111-111-1-111-1111-1-11-1
χ1511111111111111-1-11-1-11-1-1-1-11111-1-111-1-111-1-1-1-1-1-1111111-1-1-11111-1-11-1-111111-1-1-11-11-1
χ1611111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1111111-111-1-1-1-11-1-11-11-11
χ172222222222-2-2-2-22222220000-2-2-2-222002-200-2-200000000222-2-20000000000000-20000000
χ182222222222-2-2-2-22222220000-2-2-2-2-2-2002-200-2-200000000-2-2-222000000000000020000000
χ192222222222-2-2-2-2-2-22-2-220000-2-2-2-22200-22002200000000-2-22-2-2000000000000020000000
χ202222222222-2-2-2-2-2-22-2-220000-2-2-2-2-2-200-2200220000000022-2220000000000000-20000000
χ2122222-2-222200002-2-2-2-2-222−2−200002200202−20022−2−222−2−2-22-20022−2−200000000002−200000
χ2222222-2-222200002-2-2-2-2-222−2−20000-2-200202−20022−2−222−2−22-2200−2−2220000000000−2200000
χ2322222-2-222200002-2-2-2-2-2−2−2220000220020−2200−2−222−2−222-22-200−2−2220000000000−2200000
χ2422222-2-222200002-2-2-2-2-2−2−2220000-2-20020−2200−2−222−2−2222-220022−2−200000000002−200000
χ2522222-2-22220000-22-222-222−2−200002200-20−220022−2−2−2−2222-2-20022−2−20000000000−2200000
χ2622222-2-22220000-22-222-222−2−20000-2-200-20−220022−2−2−2−222-22200−2−22200000000002−200000
χ2722222-2-22220000-22-222-2−2−22200002200-202−200−2−22222−2−22-2-200−2−22200000000002−200000
χ2822222-2-22220000-22-222-2−2−2220000-2-200-202−200−2−22222−2−2-2220022−2−20000000000−2200000
χ292222-122-1-1-1222222-1-1-1-12222-1-1-1-10022-1222-1-1-1-1-1-1-1-1-1-1000000000222-1-1-1-100000-1-1000
χ302222-122-1-1-1222222-1-1-1-12222-1-1-1-100-2-2-1222-1-1-1-1-1-1-1-1-1-1000000000-2-2-211110000011000
χ312222-122-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-10022-12-2-2-1-1111111110000000002-2-2-1-1-1-10000011000
χ322222-122-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-100-2-2-12-2-2-1-111111111000000000-222111100000-1-1000
χ332222-122-1-1-12222-2-2-111-12222-1-1-1-100221-2-2-211-1-1-1-11111000000000-22-211-1-100000-11000
χ342222-122-1-1-12222-2-2-111-12222-1-1-1-100-2-21-2-2-211-1-1-1-111110000000002-22-1-111000001-1000
χ352222-122-1-1-12222-2-2-111-1-2-2-2-2-1-1-1-100221-222111111-1-1-1-1000000000-2-2211-1-1000001-1000
χ362222-122-1-1-12222-2-2-111-1-2-2-2-2-1-1-1-100-2-21-222111111-1-1-1-100000000022-2-1-11100000-11000
χ372-2-222-22-2-22-2-22200-2002000022-2-2002-200000000000000000002-22-2000002-22-200000000
χ382-2-222-22-2-22-2-22200-2002000022-2-2002-20000000000000000000-22-22000002-2-2200000000
χ392-2-222-22-2-22-2-22200-2002000022-2-200-2200000000000000000002-22-200000-22-2200000000
χ402-2-222-22-2-22-2-22200-2002000022-2-200-220000000000000000000-22-2200000-222-200000000
χ414444-244-2-2-2-4-4-4-444-2-2-2-2000022220000-2-400220000000000000000000000000000000000
χ424444-244-2-2-2-4-4-4-4-4-4-222-20000222200002400-2-20000000000000000000000000000000000
χ434444-2-4-4-2-2-200004-422222222−22−2200000000-2022−2200−2−222−2−22200000000000000000000000000
χ444444-2-4-4-2-2-200004-42222−22−22222200000000-20−22220022−2−222−2−200000000000000000000000000
χ454444-2-4-4-2-2-20000-442-2-222222−22−220000000020−222200−2−22222−2−200000000000000000000000000
χ464444-2-4-4-2-2-20000-442-2-22−22−222222000000002022−220022−2−2−2−22200000000000000000000000000
χ4744-4-44004-4-422−2222−22000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ4322−2222−220000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43000000000000000000000000000000
χ4844-4-44004-4-422−2222−220000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4322−2222−2200000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43000000000000000000000000000000
χ4944-4-44004-4-4−2222−22220000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2222−222200000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47000000000000000000000000000000
χ5044-4-44004-4-4−2222−2222000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2222−22220000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47000000000000000000000000000000
χ5144-4-4-200-22222−2222−2200023−230−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−22−22000000006−6ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300000000000000000000000000
χ5244-4-4-200-22222−2222−2200023−2302ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−22−22000000006−6−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300000000000000000000000000
χ5344-4-4-200-22222−2222−22000−23230−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−22−2200000000−66ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300000000000000000000000000
χ5444-4-4-200-22222−2222−22000−232302ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−22−2200000000−66−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300000000000000000000000000
χ5544-4-4-200-222−2222−222200023−2302ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472−22−200000000−66−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700000000000000000000000000
χ5644-4-4-200-222−2222−222200023−230−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472−22−200000000−66ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700000000000000000000000000
χ5744-4-4-200-222−2222−2222000−232302ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472−22−2000000006−6−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700000000000000000000000000
χ5844-4-4-200-222−2222−2222000−23230−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472−22−2000000006−6ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700000000000000000000000000
χ594-44-4400-44-422−22−22220000000000−222222−224-4000000000000000000022−22000000000000000000000
χ604-44-4400-44-422−22−22220000000000−222222−22-440000000000000000000−2222000000000000000000000
χ614-44-4400-44-4−222222−22000000000022−22−22224-40000000000000000000−2222000000000000000000000
χ624-44-4400-44-4−222222−22000000000022−22−2222-44000000000000000000022−22000000000000000000000
χ634-4-4444-4-4-44000000400-4000000000000000000000000000000022−22−222200000000000000000
χ644-4-4444-4-4-44000000400-40000000000000000000000000000000−222222−2200000000000000000
χ654-4-444-44-4-4444-4-400-40040000-4-44400000000000000000000000000000000000000000000
χ664-4-44-2-4422-244-4-400200-2000022-2-2000000000000000000000000000000−2i32i3000000000000
χ674-4-44-2-4422-244-4-400200-2000022-2-20000000000000000000000000000002i3−2i3000000000000
χ684-4-44-2-4422-2-4-44400200-20000-2-222004-40000000000000000000000000000-220000000000
χ694-4-44-2-4422-2-4-44400200-20000-2-22200-4400000000000000000000000000002-20000000000
χ708-88-8-4004-4442−42−4242000000000022−22−222200000000000000000000000000000000000000000000
χ718-88-8-4004-44−424242−420000000000−222222−2200000000000000000000000000000000000000000000
χ728-8-88-48-844-4000000-40040000000000000000000000000000000000000000000000000000

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