Finite Group Databasebeta

← Group #10709175

Character table — Group #10709175

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881212121212121212161616161616242424242424323232484848
order12223444466688882248812121212242424244668812121224242424242416161616161616168824242424441616161641212444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111
χ51111111111111111-1-111111111111-1-1-1-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1
χ61111111111111111-1-111111111111-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-111
χ71111111111111111-1-111111111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111
χ81111111111111111-1-111111111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9222222222222-2-2-2-2222-2-22222-2-2-2-2222-2-2222-2-2-2-2-2-200000000000000000000000000
χ10222222222222-2-2-2-2-2-22-2-22222-2-2-2-2-2-2-222-2-22-2-2222200000000000000000000000000
χ11222222-2-22222000022-2002-2-220000-22200-2-2-20000002222−2−2−2−20000000022−2−2000000
χ12222222-2-22222000022-2002-2-220000-22200-2-2-2000000−2−2−2−2222200000000−2−222000000
χ13222222-2-222220000-2-2-2002-2-2200002-2-20022-20000002222−2−2−2−200000000−2−222000000
χ14222222-2-222220000-2-2-2002-2-2200002-2-20022-2000000−2−2−2−222220000000022−2−2000000
χ1522222-222-2222222200-2-2-2-222-222220000000-2-2-2000000000000000000220000000-200
χ1622222-222-2222222200-2-2-2-222-222220000000-2-2-2000000000000000000-2-20000000200
χ1722222-222-2222-2-2-2-200-222-222-2-2-2-2-20000000-22200000000000000000000000000002-2
χ1822222-222-2222-2-2-2-200-222-222-2-2-2-2-20000000-2220000000000000000000000000000-22
χ192222-12222-1-1-1222222222-1-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000002-1-1000
χ202222-12222-1-1-1222222222-1-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-100000000-2-21111000000-211000
χ212222-12222-1-1-12222-2-2222-1-1-1-1-1-1-1-1-211-2-211-1-1-111110000000022-1-1-1-1000000-211000
χ222222-12222-1-1-12222-2-2222-1-1-1-1-1-1-1-1-211-2-211-1-1-1111100000000-2-211110000002-1-1000
χ232222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-111112-1-1-2-2-1-1-11111110000000000−i3−i3i3i30000000−i3i3000
χ242222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-111112-1-1-2-2-1-1-11111110000000000i3i3−i3−i30000000i3−i3000
χ252222-12222-1-1-1-2-2-2-2-2-22-2-2-1-1-1-11111-2112211-111-1-1-1-10000000000−i3−i3i3i30000000i3−i3000
χ262222-12222-1-1-1-2-2-2-2-2-22-2-2-1-1-1-11111-2112211-111-1-1-1-10000000000i3i3−i3−i30000000−i3i3000
χ2722-2-22200-22-2-22−22−22-202−2200-222−2−202-22−20002−222−2−2−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ4300000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43000000
χ2822-2-22200-22-2-22−22−22-202−2200-222−2−202-22−20002−222−2−2ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ4300000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43000000
χ2922-2-22200-22-2-22−22−2-2202−2200-222−2−20-22−220002−2−2−222−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ4300000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43000000
χ3022-2-22200-22-2-22−22−2-2202−2200-222−2−20-22−220002−2−2−222ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ4300000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43000000
χ3122-2-22200-22-2-2−22−222-20−22200-2−2−22202-2−22000−22−2−222ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ4700000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000000
χ3222-2-22200-22-2-2−22−222-20−22200-2−2−22202-2−22000−22−2−222−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ4700000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000000
χ3322-2-22200-22-2-2−22−22-220−22200-2−2−2220-222−2000−2222−2−2ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ4700000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000000
χ3422-2-22200-22-2-2−22−22-220−22200-2−2−2220-222−2000−2222−2−2−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ4700000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000000
χ352-22-220-220-22-2-2-222000000-2202-22-2000000000000002−22−22−22−2−i2i2−i2i2−i2i22i−2i0000000000
χ362-22-220-220-22-2-2-222000000-2202-22-2000000000000002−22−22−22−2i2−i2i2−i2i2−i2−2i2i0000000000
χ372-22-220-220-22-2-2-222000000-2202-22-200000000000000−22−22−22−22−i2i2−i2i2−i2i2−2i2i0000000000
χ382-22-220-220-22-2-2-222000000-2202-22-200000000000000−22−22−22−22i2−i2i2−i2i2−i22i−2i0000000000
χ3944444-4-4-4-4444000000400-4-4-4-400000000000400000000000000000000000000000000
χ404444-24-4-44-2-2-2000044-400-222-20000-4-2-20022200000000000000000000000000000000
χ414444-24-4-44-2-2-20000-4-4-400-222-2000042200-2-2200000000000000000000000000000000
χ424444-2-444-4-2-2-2444400-4-4-42-2-22-2-2-2-20000000222000000000000000000000000000000
χ434444-2-444-4-2-2-2-4-4-4-400-4442-2-22222200000002-2-2000000000000000000000000000000
χ444444-2-4-4-4-4-2-2-2000000400222200000000000-20023−2323−2300000000000000000000000000
χ454444-2-4-4-4-4-2-2-2000000400222200000000000-200−2323−232300000000000000000000000000
χ4644-4-44-40044-4-422−2222−22000−2222-40042222−22−2200000000−2222000000000000000000000000000000
χ4744-4-44-40044-4-4−2222−222200022−22-4004−22−2222220000000022−22000000000000000000000000000000
χ4844-4-4-2400-4-22222−2222−224-4022−22-2002−2−2220-2222−22000−22−2−22200000000000000000000000000
χ4944-4-4-2400-4-22222−2222−22-44022−22-2002−2−22202-2−2222000−2222−2−200000000000000000000000000
χ5044-4-4-2400-4-222−2222−22224-40−2222-200222−2−20-22−22220002−222−2−200000000000000000000000000
χ5144-4-4-2400-4-222−2222−2222-440−2222-200222−2−202-222−220002−2−2−22200000000000000000000000000
χ5244-4-4-2-4004-22222−2222−22000−2222200-2−2−2220000023−2302−26−6−6600000000000000000000000000
χ5344-4-4-2-4004-22222−2222−22000−2222200-2−2−22200000−232302−2−666−600000000000000000000000000
χ5444-4-4-2-4004-222−2222−222200022−22200-222−2−20000023−230−22−666−600000000000000000000000000
χ5544-4-4-2-4004-222−2222−222200022−22200-222−2−200000−23230−226−6−6600000000000000000000000000
χ564-44-4404-40-44-400000000004-400000000000000000002-22-2-22-22000000000000000000
χ574-44-4404-40-44-400000000004-40000000000000000000-22-222-22-2000000000000000000
χ584-44-440-440-44-444-4-4000000-440-44-440000000000000000000000000000000000000000
χ594-44-4-20-4402-2244-4-40000002-202-22-20000000000000000000000006−6−66000000000000
χ604-44-4-20-4402-2244-4-40000002-202-22-2000000000000000000000000−666−6000000000000
χ614-44-4-20-4402-22-4-4440000002-20-22-220000000000000000000000−2i22i2i2−i2i2−i2000000000000
χ624-44-4-20-4402-22-4-4440000002-20-22-2200000000000000000000002i2−2i2−i2i2−i2i2000000000000
χ634-4-4440000-4-4422−22−2222000000000−222222−2200000000000000ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47000000000000000000
χ644-4-4440000-4-4422−22−2222000000000−222222−2200000000000000−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47000000000000000000
χ654-4-4440000-4-44−222222−2200000000022−22−222200000000000000ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47000000000000000000
χ664-4-4440000-4-44−222222−2200000000022−22−222200000000000000−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47000000000000000000
χ678-88-8-408-804-440000000000-44000000000000000000000000000000000000000000000
χ688-8-88-4000044-442−42−424200000000022−22−22220000000000000000000000000000000000000000
χ698-8-88-4000044-4−424242−42000000000−222222−220000000000000000000000000000000000000000

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