Finite Group Databasebeta

← Group #10713976

Character table — Group #10713976

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1222223444466688886688121212122424242416161616242448484848484848481616161616161616224466661212121224882288
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
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
χ152222-2-222-22-22222222-2-2-2-22-2-2222220000-2-20000000000000000002-2000022-2-200000000
χ162222-2-222-22-22222222-2-2-2-22-2-2222220000-2-2000000000000000000-220000-2-22200000000
χ172222-2-222-22-2222-2-2-2-2-2-2222-2-22-2-2-2-2000022000000000000000000000000000000002-200
χ182222-2-222-22-2222-2-2-2-2-2-2222-2-22-2-2-2-200002200000000000000000000000000000000-2200
χ192222-2-22-22-222220000-2-200-222-2000022−2−2002222−2−2−2−22222−2−2−2−20000000000002-2000000
χ202222-2-22-22-222220000-2-200-222-2000022−2−2002222−2−2−2−2−2−2−2−22222000000000000-22000000
χ212222-2-22-22-222220000-2-200-222-20000−2−22200−2−2−2−222222222−2−2−2−2000000000000-22000000
χ222222-2-22-22-222220000-2-200-222-20000−2−22200−2−2−2−22222−2−2−2−222220000000000002-2000000
χ232222-2-2-12-22-2-1-1-1222211-2-2-111-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300000000002-2−i3−i3i3i3-1-11100000000
χ242222-2-2-12-22-2-1-1-1222211-2-2-111-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i30000000000-22i3i3−i3−i311-1-100000000
χ252222-2-2-12-22-2-1-1-1222211-2-2-111-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300000000002-2i3i3−i3−i3-1-11100000000
χ262222-2-2-12-22-2-1-1-1222211-2-2-111-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i30000000000-22−i3−i3i3i311-1-100000000
χ272-2-222-2222-2-22-2-200002-20022-2-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i222−2−222−2−2000000000000002i−2i0000
χ282-2-222-2222-2-22-2-200002-20022-2-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2−2−222−2−22200000000000000−2i2i0000
χ292-2-222-2222-2-22-2-200002-20022-2-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i222−2−222−2−200000000000000−2i2i0000
χ302-2-222-2222-2-22-2-200002-20022-2-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2−2−222−2−222000000000000002i−2i0000
χ312-2-222-22-2-2222-2-222-2-22-2-22-2-22222-2-200002-200000000000000002-2002-22-2000000000000
χ322-2-222-22-2-2222-2-222-2-22-2-22-2-22222-2-200002-20000000000000000-2200-22-22000000000000
χ332-2-222-22-2-2222-2-2-2-2222-22-2-2-222-2-2220000-2200000000000000000000000000000000002-2
χ342-2-222-22-2-2222-2-2-2-2222-22-2-2-222-2-2220000-220000000000000000000000000000000000-22
χ352-2-222-2-1-2-222-11122-2-2-11-2211-1-1-1-1110000-113−3−33−333−3000000002-200-11-113−33−300000000
χ362-2-222-2-1-2-222-11122-2-2-11-2211-1-1-1-1110000-113−3−33−333−300000000-22001-11-1−33−3300000000
χ372-2-222-2-1-2-222-11122-2-2-11-2211-1-1-1-1110000-11−333−33−3−33000000002-200-11-11−33−3300000000
χ382-2-222-2-1-2-222-11122-2-2-11-2211-1-1-1-1110000-11−333−33−3−3300000000-22001-11-13−33−300000000
χ392-2-22-222-222-22-2-222-2-2-222-2-22-2222-2-22i−2i−2i2i-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ402-2-22-222-222-22-2-222-2-2-222-2-22-2222-2-2−2i2i2i−2i-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ412-2-22-222-222-22-2-2-2-222-22-22-22-22-2-22200002-20000000022-2-2-2-22200000000000000000000
χ422-2-22-222-222-22-2-2-2-222-22-22-22-22-2-22200002-200000000-2-22222-2-200000000000000000000
χ432-2-22-22-1-222-2-11122-2-21-12-21-11-1-1-1112i−2i−2i2i1-1−ii−iii−ii−i000000000000−i3i3i3−i33−3−3300000000
χ442-2-22-22-1-222-2-11122-2-21-12-21-11-1-1-1112i−2i−2i2i1-1−ii−iii−ii−i000000000000i3−i3−i3i3−333−300000000
χ452-2-22-22-1-222-2-11122-2-21-12-21-11-1-1-111−2i2i2i−2i1-1i−ii−i−ii−ii000000000000−i3i3i3−i3−333−300000000
χ462-2-22-22-1-222-2-11122-2-21-12-21-11-1-1-111−2i2i2i−2i1-1i−ii−i−ii−ii000000000000i3−i3−i3i33−3−3300000000
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
χ49444444-2-4-4-4-4-2-2-20000-2-20022220000000000i6i6−i6−i6−i6−i6i6i60000000000000000000000000000
χ50444444-2-4-4-4-4-2-2-20000-2-20022220000000000−i6−i6i6i6i6i6−i6−i60000000000000000000000000000
χ514444-4-4-24-44-4-2-2-2-4-4-4-42244-222-222220000-2-2000000000000000000000000000000000000
χ524444-4-4-2-44-44-2-2-2000022002-2-2200002222−22−2200−2−2−2−222220000000000000000000000000000
χ534444-4-4-2-44-44-2-2-2000022002-2-220000−22−222222002222−2−2−2−20000000000000000000000000000
χ5444-4-40040000-44-422−2222−220000000022−2222−2200000000000000ζ11−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
χ5544-4-40040000-44-422−2222−220000000022−2222−2200000000000000−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
χ5644-4-40040000-44-4−2222−222200000000−2222−222200000000000000ζ11−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
χ5744-4-40040000-44-4−2222−222200000000−2222−222200000000000000−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
χ624-4-444-4-244-4-4-2220000-2200-2-2220000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ634-4-444-4-244-4-4-2220000-2200-2-22200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ644-4-444-4-2-4-444-222-4-444-224-422-2-222-2-200002-2000000000000000000000000000000000000
χ654-4-44-4444-4-444-4-40000-44004-44-40000000000000000000000000000000000000000000000
χ664-4-44-44-24-4-44-22200002-200-22-2200000000006−6−666−6−660000000000000000000000000000
χ674-4-44-44-24-4-44-22200002-200-22-220000000000−666−6−666−60000000000000000000000000000
χ684-4-44-44-2-444-4-222-4-4442-2-442-22-222-2-20000-22000000000000000000000000000000000000
χ6988-8-800-400004-4442−4242−4200000000−2222−2222000000000000000000000000000000000000000000
χ7088-8-800-400004-44−4242−42420000000022−2222−22000000000000000000000000000000000000000000
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.