Finite Group Databasebeta

← Group #10713911

Character table — Group #10713911

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444666888866881212121224242424161616162424484848484848484816161616161616164488121212122424242424882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11-1-11
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111-1-11
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1
χ922222222222222-2-2-2-222-2-22222-2-2-2-20000-2-2000000000000000000000000000022-2-20000
χ1022222222222222-2-2-2-222-2-22222-2-2-2-20000-2-20000000000000000000000000000-2-2220000
χ11222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ12222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ13222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ14222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ152222-2-222-22-22220000-2-2002-2-22000022−2−2002222−2−2−2−22222−2−2−2−20000000000002-2000000
χ162222-2-222-22-22220000-2-2002-2-22000022−2−2002222−2−2−2−2−2−2−2−22222000000000000-22000000
χ172222-2-222-22-22220000-2-2002-2-220000−2−22200−2−2−2−222222222−2−2−2−2000000000000-22000000
χ182222-2-222-22-22220000-2-2002-2-220000−2−22200−2−2−2−22222−2−2−2−222220000000000002-2000000
χ192222-2-22-22-222222222-2-2-2-2-222-222220000-2-200000000000000000000000000000000200-2
χ202222-2-22-22-222222222-2-2-2-2-222-222220000-2-200000000000000000000000000000000-2002
χ212222-2-22-22-22222-2-2-2-2-2-222-222-2-2-2-2-200002200000000000000002-20022-2-2000000000000
χ222222-2-22-22-22222-2-2-2-2-2-222-222-2-2-2-2-20000220000000000000000-2200-2-222000000000000
χ232222-2-2-1-22-22-1-1-1-2-2-2-211221-1-1111110000-1-133−3−333−3−3000000002-200-1-11133−3−300000000
χ242222-2-2-1-22-22-1-1-1-2-2-2-211221-1-1111110000-1-133−3−333−3−300000000-220011-1-1−3−33300000000
χ252222-2-2-1-22-22-1-1-1-2-2-2-211221-1-1111110000-1-1−3−333−3−333000000002-200-1-111−3−33300000000
χ262222-2-2-1-22-22-1-1-1-2-2-2-211221-1-1111110000-1-1−3−333−3−33300000000-220011-1-133−3−300000000
χ272-2-222-2222-2-2-22-200002-20022-2-200002−22−2002−22−22−22−2−i2−i2i2i2−i2−i2i2i2000000000000002i−2i0000
χ282-2-222-2222-2-2-22-200002-20022-2-200002−22−2002−22−22−22−2i2i2−i2−i2i2i2−i2−i200000000000000−2i2i0000
χ292-2-222-2222-2-2-22-200002-20022-2-20000−22−2200−22−22−22−22−i2−i2i2i2−i2−i2i2i200000000000000−2i2i0000
χ302-2-222-2222-2-2-22-200002-20022-2-20000−22−2200−22−22−22−22i2i2−i2−i2i2i2−i2−i2000000000000002i−2i0000
χ312-2-222-22-2-222-22-222-2-22-2-22-2-22222-2-200002-20000000000000000002-200002-22-200000000
χ322-2-222-22-2-222-22-222-2-22-2-22-2-22222-2-200002-2000000000000000000-220000-22-2200000000
χ332-2-222-22-2-222-22-2-2-2222-22-2-2-222-2-2220000-220000000000000000000000000000000002-20
χ342-2-222-22-2-222-22-2-2-2222-22-2-2-222-2-2220000-22000000000000000000000000000000000-220
χ352-2-222-2-1-2-2221-1122-2-2-11-2211-1-1-1-1110000-113−3−33−333−300000000002-23−33−3-11-1100000000
χ362-2-222-2-1-2-2221-1122-2-2-11-2211-1-1-1-1110000-113−3−33−333−30000000000-22−33−331-11-100000000
χ372-2-222-2-1-2-2221-1122-2-2-11-2211-1-1-1-1110000-11−333−33−3−3300000000002-2−33−33-11-1100000000
χ382-2-222-2-1-2-2221-1122-2-2-11-2211-1-1-1-1110000-11−333−33−3−330000000000-223−33−31-11-100000000
χ392-2-22-2222-2-22-22-222-2-2-222-22-22-222-2-20000-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ402-2-22-2222-2-22-22-222-2-2-222-22-22-222-2-20000-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ412-2-22-2222-2-22-22-2-2-222-22-222-22-2-2-2222-2-222-22-22-2-22-220000000000000000000000000000
χ422-2-22-2222-2-22-22-2-2-222-22-222-22-2-2-222-222-22-2-22-222-22-20000000000000000000000000000
χ432-2-22-22-12-2-221-11-2-2221-1-22-11-1111-1-12-2-22-11-11-111-11-10000000000003−3−33−333−300000000
χ442-2-22-22-12-2-221-11-2-2221-1-22-11-1111-1-12-2-22-11-11-111-11-1000000000000−333−33−3−3300000000
χ452-2-22-22-12-2-221-11-2-2221-1-22-11-1111-1-1-222-2-111-11-1-11-110000000000003−3−333−3−3300000000
χ462-2-22-22-12-2-221-11-2-2221-1-22-11-1111-1-1-222-2-111-11-1-11-11000000000000−333−3−333−300000000
χ474444444-4-4-4-444400004400-4-4-4-40000000000000000000000000000000000000000000000
χ48444444-24444-2-2-2-4-4-4-4-2-2-4-4-2-2-2-22222000022000000000000000000000000000000000000
χ49444444-2-4-4-4-4-2-2-20000-2-2002222000000000066−6−6−6−6660000000000000000000000000000
χ50444444-2-4-4-4-4-2-2-20000-2-20022220000000000−6−66666−6−60000000000000000000000000000
χ514444-4-4-24-44-4-2-2-200002200-222-200002222−22−2200−2−2−2−222220000000000000000000000000000
χ524444-4-4-24-44-4-2-2-200002200-222-20000−22−222222002222−2−2−2−20000000000000000000000000000
χ534444-4-4-2-44-44-2-2-2444422-4-42-2-22-2-2-2-2000022000000000000000000000000000000000000
χ5444-4-400400004-4-422−2222−220000000022−2222−2200000000000000ζ11−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−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ4700000000000000000000
χ5544-4-400400004-4-422−2222−220000000022−2222−2200000000000000−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+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−ζ4700000000000000000000
χ5644-4-400400004-4-4−2222−222200000000−2222−222200000000000000ζ11−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+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ4700000000000000000000
χ5744-4-400400004-4-4−2222−222200000000−2222−222200000000000000−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−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ4700000000000000000000
χ584-44-40040000-4-4422−22−22220000000022−22−222200000000000000ζ11+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+ζ4700000000000000000000
χ594-44-40040000-4-4422−22−22220000000022−22−222200000000000000−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−ζ4700000000000000000000
χ604-44-40040000-4-44−222222−2200000000−222222−2200000000000000ζ11+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+ζ4700000000000000000000
χ614-44-40040000-4-44−222222−2200000000−222222−2200000000000000−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−ζ4700000000000000000000
χ624-4-444-4-244-4-42-220000-2200-2-222000022−2222−2200−22−22−22−220000000000000000000000000000
χ634-4-444-4-244-4-42-220000-2200-2-2220000−2222−2222002−22−22−22−20000000000000000000000000000
χ644-4-444-4-2-4-4442-22-4-444-224-422-2-222-2-200002-2000000000000000000000000000000000000
χ654-4-44-444-444-4-44-40000-4400-44-440000000000000000000000000000000000000000000000
χ664-4-44-44-24-4-442-2244-4-42-24-4-22-22-2-22200002-2000000000000000000000000000000000000
χ674-4-44-44-2-444-42-2200002-2002-22-200000000006−6−666−6−660000000000000000000000000000
χ684-4-44-44-2-444-42-2200002-2002-22-20000000000−666−6−666−60000000000000000000000000000
χ6988-8-800-40000-44442−4242−4200000000−2222−2222000000000000000000000000000000000000000000
χ7088-8-800-40000-444−4242−42420000000022−2222−22000000000000000000000000000000000000000000
χ718-88-800-4000044-442−42−424200000000−222222−22000000000000000000000000000000000000000000
χ728-88-800-4000044-4−424242−420000000022−22−2222000000000000000000000000000000000000000000

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