Finite Group Databasebeta

← Group #10709245

Character table — Group #10709245

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881212121212121212161616161616242424242424323232484848
order1222344446668888444881212121224242424488121212121224242424242416161616161616168824242424221616161641212444
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
χ511111111111111111-1-11111111111-1-1-1-1-11-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1
χ611111111111111111-1-11111111111-1-1-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-111
χ711111111111111111-1-11111111111-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111
χ811111111111111111-1-11111111111-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9222222222222-2-2-2-2222-2-22222-2-2-2-22-2-222222-2-2-2-2-2-200000000000000000000000000
χ10222222222222-2-2-2-22-2-2-2-22222-2-2-2-2-222-2-22-2-2-2-2222200000000000000000000000000
χ11222222-2-222220000-222002-2-220000-20022-2-2-20000002222−2−2−2−20000000022−2−2000000
χ12222222-2-222220000-222002-2-220000-20022-2-2-2000000−2−2−2−2222200000000−2−222000000
χ13222222-2-222220000-2-2-2002-2-220000200-2-2-2220000002222−2−2−2−200000000−2−222000000
χ14222222-2-222220000-2-2-2002-2-220000200-2-2-222000000−2−2−2−222220000000022−2−2000000
χ1522222-222-22222222-200-2-2-222-2222200000-200-2-2000000000000000000220000000-200
χ1622222-222-22222222-200-2-2-222-2222200000-200-2-2000000000000000000-2-20000000200
χ1722222-222-2222-2-2-2-2-20022-222-2-2-2-2-200000-2002200000000000000000000000000002-2
χ1822222-222-2222-2-2-2-2-20022-222-2-2-2-2-200000-200220000000000000000000000000000-22
χ192222-12222-1-1-1222222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000002-1-1000
χ202222-12222-1-1-1222222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-100000000-2-21111000000-211000
χ212222-12222-1-1-122222-2-222-1-1-1-1-1-1-1-1-2-2-211-111-1-111110000000022-1-1-1-1000000-211000
χ222222-12222-1-1-122222-2-222-1-1-1-1-1-1-1-1-2-2-211-111-1-1111100000000-2-211110000002-1-1000
χ232222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-111112-2-2-1-1-1-1-11111110000000000−i3−i3i3i30000000−i3i3000
χ242222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-111112-2-2-1-1-1-1-11111110000000000i3i3−i3−i30000000i3−i3000
χ252222-12222-1-1-1-2-2-2-22-2-2-2-2-1-1-1-11111-22211-11111-1-1-1-10000000000−i3−i3i3i30000000i3−i3000
χ262222-12222-1-1-1-2-2-2-22-2-2-2-2-1-1-1-11111-22211-11111-1-1-1-10000000000i3i3−i3−i30000000−i3i3000
χ2722-2-2202-202-2-222-2-20000002-2022-2-20000000000000022−2−222−2−22−22−22−22-20000000000
χ2822-2-2202-202-2-222-2-20000002-2022-2-20000000000000022−2−222−2−2−22−22−22-220000000000
χ2922-2-2202-202-2-222-2-20000002-2022-2-200000000000000−2−222−2−2222−22−22−2-220000000000
χ3022-2-2202-202-2-222-2-20000002-2022-2-200000000000000−2−222−2−222−22−22−222-20000000000
χ312-2-222200-2-22-22−22−202-22−2200-22−22−202−22-20002−222−2−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ4300000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000
χ322-2-222200-2-22-22−22−202-22−2200-22−22−202−22-20002−222−2−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ4300000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000
χ332-2-222200-2-22-22−22−20-222−2200-22−22−20−22-220002−2−2−222−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ4300000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000
χ342-2-222200-2-22-22−22−20-222−2200-22−22−20−22-220002−2−2−222ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ4300000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000
χ352-2-222200-2-22-2−22−2202-2−22200-2−22−220−222-2000−22−2−222ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ4700000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000
χ362-2-222200-2-22-2−22−2202-2−22200-2−22−220−222-2000−22−2−222−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ4700000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000
χ372-2-222200-2-22-2−22−220-22−22200-2−22−2202−2-22000−2222−2−2ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ4700000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000
χ382-2-222200-2-22-2−22−220-22−22200-2−22−2202−2-22000−2222−2−2−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ4700000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000
χ3944444-4-4-4-4444000040000-4-4-4-400000000040000000000000000000000000000000000
χ404444-24-4-44-2-2-20000-44400-222-20000-400-2-222200000000000000000000000000000000
χ414444-24-4-44-2-2-20000-4-4-400-222-20000400222-2-200000000000000000000000000000000
χ424444-2-444-4-2-2-24444-400-4-42-2-22-2-2-2-20000020022000000000000000000000000000000
χ434444-2-444-4-2-2-2-4-4-4-4-400442-2-22222200000200-2-2000000000000000000000000000000
χ444444-2-4-4-4-4-2-2-20000400002222000000000-2000023−2323−2300000000000000000000000000
χ454444-2-4-4-4-4-2-2-20000400002222000000000-20000−2323−232300000000000000000000000000
χ4644-4-4404-404-4-4-4-4440000004-40-4-4440000000000000000000000000000000000000000
χ4744-4-440-4404-4-40000000000-44000000000000000000022-2-2-2-222000000000000000000
χ4844-4-440-4404-4-40000000000-440000000000000000000-2-22222-2-2000000000000000000
χ4944-4-4-204-40-22244-4-4000000-220-2-222000000000000000000000022−22−22−22000000000000
χ5044-4-4-204-40-22244-4-4000000-220-2-2220000000000000000000000−22222−22−2000000000000
χ5144-4-4-204-40-222-4-444000000-22022-2-2000000000000000000000000i6−i6−i6i6000000000000
χ5244-4-4-204-40-222-4-444000000-22022-2-2000000000000000000000000−i6i6i6−i6000000000000
χ534-44-440000-4-4422−22−222200000000022−22−222200000000000000ζ11+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−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
χ544-44-440000-4-4422−22−222200000000022−22−222200000000000000−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+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
χ554-44-440000-4-44−222222−22000000000−222222−2200000000000000ζ11+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+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
χ564-44-440000-4-44−222222−22000000000−222222−2200000000000000−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−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
χ574-4-444-4004-44-422−2222−22000−2222-400422−2222−2200000000−2222000000000000000000000000000000
χ584-4-444-4004-44-4−2222−222200022−22-4004−2222−22220000000022−22000000000000000000000000000000
χ594-4-44-2400-42-2222−2222−2204-422−22-2002−22−22022−22-22000−22−2−22200000000000000000000000000
χ604-4-44-2400-42-2222−2222−220-4422−22-2002−22−220−22222-2000−2222−2−200000000000000000000000000
χ614-4-44-2400-42-22−2222−222204-4−2222-20022−22−20−2222-220002−222−2−200000000000000000000000000
χ624-4-44-2400-42-22−2222−22220-44−2222-20022−22−2022−222-20002−2−2−22200000000000000000000000000
χ634-4-44-2-40042-2222−2222−22000−2222200-2−22−2200000023−232−26−6−6600000000000000000000000000
χ644-4-44-2-40042-2222−2222−22000−2222200-2−22−22000000−23232−2−666−600000000000000000000000000
χ654-4-44-2-40042-22−2222−222200022−22200-22−22−200000023−23−22−666−600000000000000000000000000
χ664-4-44-2-40042-22−2222−222200022−22200-22−22−2000000−2323−226−6−6600000000000000000000000000
χ6788-8-8-40-880-44400000000004-4000000000000000000000000000000000000000000000
χ688-88-8-4000044-442−42−4242000000000−222222−220000000000000000000000000000000000000000
χ698-88-8-4000044-4−424242−4200000000022−22−22220000000000000000000000000000000000000000

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