Finite Group Databasebeta

← Group #10713977

Character table — Group #10713977

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444666888866881212121224242424246688121224242424242416161616161616162244666612121212161616162288
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ922222222222222-2-2-2-222-2-22222-2-2-2-22222-2-222-2-2-2-2-2-20000000000000000000000000000
χ1022222222222222-2-2-2-222-2-22222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000
χ11222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ12222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ13222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-211-2-211-1-111110000000022-2-2-1-1-1-1111100000000
χ14222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-211-2-211-1-1111100000000-2-2221111-1-1-1-100000000
χ15222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-1111122-1-1-2-2-1-1111111000000000000−i3−i3i3i3−i3−i3i3i300000000
χ16222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-1111122-1-1-2-2-1-1111111000000000000i3i3−i3−i3i3i3−i3−i300000000
χ17222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-11111-2-211221111-1-1-1-1000000000000−i3−i3i3i3i3i3−i3−i300000000
χ18222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-11111-2-211221111-1-1-1-1000000000000i3i3−i3−i3−i3−i3i3i300000000
χ192222-2-222-22-22222222-2-2-2-22-2-22222200000000-2-2000000000000002-200002-22-200000000
χ202222-2-222-22-22222222-2-2-2-22-2-22222200000000-2-200000000000000-220000-22-2200000000
χ212222-2-222-22-2222-2-2-2-2-2-2222-2-22-2-2-2-200000000220000000000002-2002-22-2000000000000
χ222222-2-222-22-2222-2-2-2-2-2-2222-2-22-2-2-2-20000000022000000000000-2200-22-22000000000000
χ232222-2-22-22-222220000-2-200-222-200002-22200-2-20000002222−2−2−2−200000000000022−2−20000
χ242222-2-22-22-222220000-2-200-222-200002-22200-2-2000000−2−2−2−22222000000000000−2−2220000
χ252222-2-22-22-222220000-2-200-222-20000-22-2-200220000002222−2−2−2−2000000000000−2−2220000
χ262222-2-22-22-222220000-2-200-222-20000-22-2-20022000000−2−2−2−2222200000000000022−2−20000
χ272222-2-2-12-22-2-1-1-1222211-2-2-111-1-1-1-1-100−i3i300−i3i311−i3−i3i3i300000000002-2−i3i3i3−i3-11-1100000000
χ282222-2-2-12-22-2-1-1-1222211-2-2-111-1-1-1-1-100−i3i300−i3i311−i3−i3i3i30000000000-22i3−i3−i3i31-11-100000000
χ292222-2-2-12-22-2-1-1-1222211-2-2-111-1-1-1-1-100i3−i300i3−i311i3i3−i3−i300000000002-2i3−i3−i3i3-11-1100000000
χ302222-2-2-12-22-2-1-1-1222211-2-2-111-1-1-1-1-100i3−i300i3−i311i3i3−i3−i30000000000-22−i3i3i3−i31-11-100000000
χ312222-2-2-12-22-2-1-1-1-2-2-2-21122-111-1111100−i3i300−i3i3-1-1i3i3−i3−i3000000002-200-11-11−i3i3i3−i300000000
χ322222-2-2-12-22-2-1-1-1-2-2-2-21122-111-1111100−i3i300−i3i3-1-1i3i3−i3−i300000000-22001-11-1i3−i3−i3i300000000
χ332222-2-2-12-22-2-1-1-1-2-2-2-21122-111-1111100i3−i300i3−i3-1-1−i3−i3i3i3000000002-200-11-11i3−i3−i3i300000000
χ342222-2-2-12-22-2-1-1-1-2-2-2-21122-111-1111100i3−i300i3−i3-1-1−i3−i3i3i300000000-22001-11-1−i3i3i3−i300000000
χ3522-2-22-2222-2-22-2-200002-20022-2-2000000002i−2i00002i−2i2i−2i22−2−222−2−2000000000000−i2i2−i2i20000
χ3622-2-22-2222-2-22-2-200002-20022-2-2000000002i−2i00002i−2i2i−2i−2−222−2−222000000000000i2−i2i2−i20000
χ3722-2-22-2222-2-22-2-200002-20022-2-200000000−2i2i0000−2i2i−2i2i22−2−222−2−2000000000000i2−i2i2−i20000
χ3822-2-22-2222-2-22-2-200002-20022-2-200000000−2i2i0000−2i2i−2i2i−2−222−2−222000000000000−i2i2−i2i20000
χ3922-2-22-22-2-2222-2-222-2-22-2-22-2-22222-2-2000000002-200000000000000000000000000002-200
χ4022-2-22-22-2-2222-2-222-2-22-2-22-2-22222-2-2000000002-20000000000000000000000000000-2200
χ4122-2-22-22-2-2222-2-2-2-2222-22-2-2-222-2-22200000000-220000000000000000000000000000002-2
χ4222-2-22-22-2-2222-2-2-2-2222-22-2-2-222-2-22200000000-22000000000000000000000000000000-22
χ4322-2-2-222-222-22-2-222-2-2-222-2-22-2222-2-200000000-220000000000000000000000002i−2i−2i2i0000
χ4422-2-2-222-222-22-2-222-2-2-222-2-22-2222-2-200000000-22000000000000000000000000−2i2i2i−2i0000
χ4522-2-2-222-222-22-2-2-2-222-22-22-22-22-2-222000000002-2000022-2-2-2-22200000000000000000000
χ4622-2-2-222-222-22-2-2-2-222-22-22-22-22-2-222000000002-20000-2-22222-2-200000000000000000000
χ474444444-4-4-4-444400004400-4-4-4-40000000000000000000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-20000-2-2002222000000−2i32i3002i3−2i30000000000000000000000000000000000
χ49444444-2-4-4-4-4-2-2-20000-2-20022220000002i3−2i300−2i32i30000000000000000000000000000000000
χ504444-4-4-2-44-44-2-2-2000022002-2-2200004-4-2-200220000000000000000000000000000000000
χ514444-4-4-2-44-44-2-2-2000022002-2-220000-442200-2-20000000000000000000000000000000000
χ5244-4-44-4-244-4-4-2220000-2200-2-222000000004i−4i0000−2i2i−2i2i0000000000000000000000000000
χ5344-4-44-4-244-4-4-2220000-2200-2-22200000000−4i4i00002i−2i2i−2i0000000000000000000000000000
χ5444-4-44-4-2-4-444-22244-4-4-22-4422-2-2-2-22200000000-2200000000000000000000000000000000
χ5544-4-44-4-2-4-444-222-4-444-224-422-2-222-2-2000000002-200000000000000000000000000000000
χ5644-4-4-4444-4-444-4-40000-44004-44-40000000000000000000000000000000000000000000000
χ5744-4-4-44-24-4-44-22200002-200-22-220000000000000023−23−23230000000000000000000000000000
χ5844-4-4-44-24-4-44-22200002-200-22-2200000000000000−232323−230000000000000000000000000000
χ5944-4-4-44-2-444-4-22244-4-42-24-42-22-2-2-222000000002-200000000000000000000000000000000
χ6044-4-4-44-2-444-4-222-4-4442-2-442-22-222-2-200000000-2200000000000000000000000000000000
χ614-44-40040000-44-422−2222−220000000022−2222−2200000000000000ζ11−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
χ624-44-40040000-44-422−2222−220000000022−2222−2200000000000000−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
χ634-44-40040000-44-4−2222−222200000000−2222−222200000000000000ζ11−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
χ644-44-40040000-44-4−2222−222200000000−2222−222200000000000000−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
χ654-4-440040000-4-4422−22−22220000000022−22−222200000000000000ζ11−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
χ664-4-440040000-4-4422−22−22220000000022−22−222200000000000000−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
χ674-4-440040000-4-44−222222−2200000000−222222−2200000000000000ζ11−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
χ684-4-440040000-4-44−222222−2200000000−222222−2200000000000000−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
χ698-88-800-400004-4442−4242−4200000000−2222−2222000000000000000000000000000000000000000000
χ708-88-800-400004-44−4242−42420000000022−2222−22000000000000000000000000000000000000000000
χ718-8-8800-4000044-442−42−424200000000−222222−22000000000000000000000000000000000000000000
χ728-8-8800-4000044-4−424242−420000000022−22−2222000000000000000000000000000000000000000000

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