Finite Group Databasebeta

← Group #70599

Character table — Group #70599

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1111222222222222222244444444444444488888888888812121212121212124848
order1222223446666666888848812121212242424242424242444441212121212121212161616161616161624
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-11111-1-1-1-1111111-1-1-11-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1
χ61111-1-11111-1-1-1-1111111-1-1-11-1-111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11
χ71111-1-11111-1-1-1-1111111-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11
χ81111-1-11111-1-1-1-1111111-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1
χ92222222222222222-2-2-2-22-2-22222-2-2-2-2-2-2-2-20000000000000000000000
χ102222222-2-222222220000-200-2-2-2-20000000000000000000022−2−222−2−200
χ112222222-2-222222220000-200-2-2-2-200000000000000000000−2−222−2−22200
χ12222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ13222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ14222222-122-1-1-1-1-1-1-1-2-2-2-22-2-2-1-1-1-1111111110000−i3−i3i3i3−i3−i3i3i30000000000
χ15222222-122-1-1-1-1-1-1-1-2-2-2-22-2-2-1-1-1-1111111110000i3i3−i3−i3i3i3−i3−i30000000000
χ162222-2-22222-2-2-2-222-2-2-2-2-2222-2-22-2-2-2-222220000000000000000000000
χ172222-2-22-2-22-2-2-2-2220000200-222-20000000000000000000022−2−2−2−22200
χ182222-2-22-2-22-2-2-2-2220000200-222-200000000000000000000−2−22222−2−200
χ192222-2-2-122-11111-1-12222-2-2-2-111-1-1-1-1-1111122-2-2-1-1-1-111110000000000
χ202222-2-2-122-11111-1-12222-2-2-2-111-1-1-1-1-11111-2-2221111-1-1-1-10000000000
χ212222-2-2-122-11111-1-1-2-2-2-2-222-111-11111-1-1-1-10000−i3−i3i3i3i3i3−i3−i30000000000
χ222222-2-2-122-11111-1-1-2-2-2-2-222-111-11111-1-1-1-10000i3i3−i3−i3−i3−i3i3i30000000000
χ232-22-2002-22-200002-222-2-2000-200222-2-20000002i−2i00002i−2i2i−2i0000000000
χ242-22-2002-22-200002-222-2-2000-200222-2-2000000−2i2i0000−2i2i−2i2i0000000000
χ252-22-2002-22-200002-2-2-222000-2002-2-22200002i−2i002i−2i2i−2i00000000000000
χ262-22-2002-22-200002-2-2-222000-2002-2-2220000−2i2i00−2i2i−2i2i00000000000000
χ272-22-200-1-221−i3−i3i3i3-1122-2-20001−i3i3-1-1-111−i3−i3i3i3002i−2i3−3−33−ii−ii0000000000
χ282-22-200-1-221−i3−i3i3i3-1122-2-20001−i3i3-1-1-111−i3−i3i3i300−2i2i−333−3i−ii−i0000000000
χ292-22-200-1-221−i3−i3i3i3-11-2-2220001−i3i3-111-1-1i3i3−i3−i32i−2i00−ii−ii3−3−330000000000
χ302-22-200-1-221−i3−i3i3i3-11-2-2220001−i3i3-111-1-1i3i3−i3−i3−2i2i00i−ii−i−333−30000000000
χ312-22-200-1-221i3i3−i3−i3-1122-2-20001i3−i3-1-1-111i3i3−i3−i3002i−2i−333−3−ii−ii0000000000
χ322-22-200-1-221i3i3−i3−i3-1122-2-20001i3−i3-1-1-111i3i3−i3−i300−2i2i3−3−33i−ii−i0000000000
χ332-22-200-1-221i3i3−i3−i3-11-2-2220001i3−i3-111-1-1−i3−i3i3i32i−2i00−ii−ii−333−30000000000
χ342-22-200-1-221i3i3−i3−i3-11-2-2220001i3−i3-111-1-1−i3−i3i3i3−2i2i00i−ii−i3−3−330000000000
χ352-2-222-2200-22-22-2-222−22−202−200002−22−22−22−2000000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300
χ362-2-222-2200-22-22-2-222−22−202−200002−22−22−22−2000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300
χ372-2-222-2200-22-22-2-22−22−220−220000−22−22−22−22000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700
χ382-2-222-2200-22-22-2-22−22−220−220000−22−22−22−22000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700
χ392-2-22-22200-2-22-22-222−22−20−2200002−22−2−22−22000000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300
χ402-2-22-22200-2-22-22-222−22−20−2200002−22−2−22−22000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300
χ412-2-22-22200-2-22-22-22−22−2202−20000−22−222−22−2000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700
χ422-2-22-22200-2-22-22-22−22−2202−20000−22−222−22−2000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700
χ43444444-2-4-4-2-2-2-2-2-2-20000-4002222000000000000000000000000000000
χ444444-4-4-2-4-4-22222-2-200004002-2-22000000000000000000000000000000
χ4544-4-40040040000-4-422−22−2222000000022−22−222200000000000000000000000000
χ4644-4-40040040000-4-4−222222−220000000−222222−2200000000000000000000000000
χ4744-4-400-200-2−2i32i32i3−2i32222−22−22220000000−222−2−i6i6i6−i60000000000000000000000
χ4844-4-400-200-2−2i32i32i3−2i322−222222−2200000002−2−22i6−i6−i6i60000000000000000000000
χ4944-4-400-200-22i3−2i3−2i32i32222−22−22220000000−222−2i6−i6−i6i60000000000000000000000
χ5044-4-400-200-22i3−2i3−2i32i322−222222−2200000002−2−22−i6i6i6−i60000000000000000000000
χ514-44-40044-4-400004-40000000400-4000000000000000000000000000000
χ524-44-400-24-42−2i3−2i32i32i3-220000000-22i3−2i32000000000000000000000000000000
χ534-44-400-24-422i32i3−2i3−2i3-220000000-2−2i32i32000000000000000000000000000000
χ544-4-444-4-2002-22-222-222−2222−22022−220000−22−22−22−220000000000000000000000
χ554-4-444-4-2002-22-222-2−2222−22220−222200002−22−22−22−20000000000000000000000
χ564-4-44-44-20022-22-22-222−2222−220−22220000−22−222−22−20000000000000000000000
χ574-4-44-44-20022-22-22-2−2222−2222022−2200002−22−2−22−220000000000000000000000

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