Finite Group Databasebeta

← Group #10714398

Character table — Group #10714398

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order122222344446668888668812121212242424242466881212242424242424161616161616161644881212121224242424161616164444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111
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
χ192222-2-222-22-22220000-2-2002-22-200002-22200-2-20000002222−2−2−2−200000000000022−2−20000
χ202222-2-222-22-22220000-2-2002-22-200002-22200-2-2000000−2−2−2−22222000000000000−2−2220000
χ212222-2-222-22-22220000-2-2002-22-20000-22-2-200220000002222−2−2−2−2000000000000−2−2220000
χ222222-2-222-22-22220000-2-2002-22-20000-22-2-20022000000−2−2−2−2222200000000000022−2−20000
χ232222-2-22-22-222222222-2-2-2-2-22-22222200000000-2-200000000000000000000000000002-200
χ242222-2-22-22-222222222-2-2-2-2-22-22222200000000-2-20000000000000000000000000000-2200
χ252222-2-22-22-22222-2-2-2-2-2-222-22-22-2-2-2-200000000220000000000000000000000000000002-2
χ262222-2-22-22-22222-2-2-2-2-2-222-22-22-2-2-2-20000000022000000000000000000000000000000-22
χ272-2-222-222-2-22-22-222-2-22-2-222-2-2222-2-2000000002-2000000000000002i−2i00002i−2i2i−2i00000000
χ282-2-222-222-2-22-22-222-2-22-2-222-2-2222-2-2000000002-200000000000000−2i2i0000−2i2i−2i2i00000000
χ292-2-222-222-2-22-22-2-2-2222-22-22-2-22-2-22200000000-220000000000002i−2i002i−2i2i−2i000000000000
χ302-2-222-222-2-22-22-2-2-2222-22-22-2-22-2-22200000000-22000000000000−2i2i00−2i2i−2i2i000000000000
χ312-2-222-22-222-2-22-200002-200-222-2000000002i−2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i20000000000002−22−20000
χ322-2-222-22-222-2-22-200002-200-222-2000000002i−2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2000000000000−22−220000
χ332-2-222-22-222-2-22-200002-200-222-200000000−2i2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2000000000000−22−220000
χ342-2-222-22-222-2-22-200002-200-222-200000000−2i2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i20000000000002−22−20000
χ352-2-222-2-12-2-221-1122-2-2-11-22-111-1-1-11100−i3i300−i3i3-11−i3i3−i3i300000000002i−2i3−3−33−ii−ii00000000
χ362-2-222-2-12-2-221-1122-2-2-11-22-111-1-1-11100−i3i300−i3i3-11−i3i3−i3i30000000000−2i2i−333−3i−ii−i00000000
χ372-2-222-2-12-2-221-1122-2-2-11-22-111-1-1-11100i3−i300i3−i3-11i3−i3i3−i300000000002i−2i−333−3−ii−ii00000000
χ382-2-222-2-12-2-221-1122-2-2-11-22-111-1-1-11100i3−i300i3−i3-11i3−i3i3−i30000000000−2i2i3−3−33i−ii−i00000000
χ392-2-222-2-12-2-221-11-2-222-112-2-111-111-1-100−i3i300−i3i31-1i3−i3i3−i3000000002i−2i00−ii−ii3−3−3300000000
χ402-2-222-2-12-2-221-11-2-222-112-2-111-111-1-100−i3i300−i3i31-1i3−i3i3−i300000000−2i2i00i−ii−i−333−300000000
χ412-2-222-2-12-2-221-11-2-222-112-2-111-111-1-100i3−i300i3−i31-1−i3i3−i3i3000000002i−2i00−ii−ii−333−300000000
χ422-2-222-2-12-2-221-11-2-222-112-2-111-111-1-100i3−i300i3−i31-1−i3i3−i3i300000000−2i2i00i−ii−i3−3−3300000000
χ432-2-22-222-2-222-22-222-2-2-222-2-2-22222-2-200000000-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ442-2-22-222-2-222-22-222-2-2-222-2-2-22222-2-200000000-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ452-2-22-222-2-222-22-2-2-222-22-22-2-222-2-222000000002-20000000000000000000000002-2-220000
χ462-2-22-222-2-222-22-2-2-222-22-22-2-222-2-222000000002-2000000000000000000000000-222-20000
χ474444444-4-4-4-444400004400-4-4-4-40000000000000000000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-20000-2-20022220000000000000023−23−23230000000000000000000000000000
χ49444444-2-4-4-4-4-2-2-20000-2-200222200000000000000−232323−230000000000000000000000000000
χ504444-4-4-24-44-4-2-2-200002200-22-2200004-4-2-200220000000000000000000000000000000000
χ514444-4-4-24-44-4-2-2-200002200-22-220000-442200-2-20000000000000000000000000000000000
χ524444-4-4-2-44-44-2-2-2444422-4-42-22-2-2-2-2-2000000002200000000000000000000000000000000
χ534444-4-4-2-44-44-2-2-2-4-4-4-422442-22-2222200000000-2-200000000000000000000000000000000
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
χ624-4-444-4-2-444-42-220000-22002-2-22000000004i−4i0000−2i−2i2i2i0000000000000000000000000000
χ634-4-444-4-2-444-42-220000-22002-2-2200000000−4i4i00002i2i−2i−2i0000000000000000000000000000
χ644-4-44-44444-4-4-44-40000-440044-4-40000000000000000000000000000000000000000000000
χ654-4-44-44-244-4-42-2200002-200-2-222000000−2i32i3002i3−2i30000000000000000000000000000000000
χ664-4-44-44-244-4-42-2200002-200-2-2220000002i3−2i300−2i32i30000000000000000000000000000000000
χ674-4-44-44-2-4-4442-2244-4-42-24-422-2-2-2-222000000002-200000000000000000000000000000000
χ684-4-44-44-2-4-4442-22-4-4442-2-4422-2-222-2-200000000-2200000000000000000000000000000000
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.