Finite Group Databasebeta

← Group #10714558

Character table — Group #10714558

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order122222344446668888668812121212242424241616161624244848484848484848161616161616161624446612121212121244884488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-111
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
χ13222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111000000002-2-22-1-1-1-1111100000000
χ14222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-222-21111-1-1-1-100000000
χ152222-2-222-2-222220000-2-20022-2-2000022−2−2002222−2−2−2−22222−2−2−2−20000000000002-2000000
χ162222-2-222-2-222220000-2-20022-2-2000022−2−2002222−2−2−2−2−2−2−2−22222000000000000-22000000
χ172222-2-222-2-222220000-2-20022-2-20000−2−22200−2−2−2−222222222−2−2−2−2000000000000-22000000
χ182222-2-222-2-222220000-2-20022-2-20000−2−22200−2−2−2−22222−2−2−2−222220000000000002-2000000
χ192222-2-22-222-22222222-2-2-2-2-2-22222220000-2-20000000000000000200-222-2-2000000000000
χ202222-2-22-222-22222222-2-2-2-2-2-22222220000-2-20000000000000000-2002-2-222000000000000
χ212222-2-22-222-2222-2-2-2-2-2-222-2-222-2-2-2-2000022000000000000000000000000000000002-200
χ222222-2-22-222-2222-2-2-2-2-2-222-2-222-2-2-2-200002200000000000000000000000000000000-2200
χ232222-2-2-1-222-2-1-1-1222211-2-211-1-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300000000200-2-1-111−i3−i3i3i300000000
χ242222-2-2-1-222-2-1-1-1222211-2-211-1-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300000000-200211-1-1i3i3−i3−i300000000
χ252222-2-2-1-222-2-1-1-1222211-2-211-1-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300000000200-2-1-111i3i3−i3−i300000000
χ262222-2-2-1-222-2-1-1-1222211-2-211-1-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300000000-200211-1-1−i3−i3i3i300000000
χ272-2-222-2222-2-2-22-222-2-22-2-222-2-2222-2-22i−2i2i−2i2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ282-2-222-2222-2-2-22-222-2-22-2-222-2-2222-2-2−2i2i−2i2i2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ292-2-222-2222-2-2-22-2-2-2222-22-22-2-22-2-2220000-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ302-2-222-2222-2-2-22-2-2-2222-22-22-2-22-2-2220000-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ312-2-222-2-122-2-21-1122-2-2-11-22-111-1-1-1112i−2i2i−2i-11−ii−ii−ii−ii000000000000−i3i3−i3i33−33−300000000
χ322-2-222-2-122-2-21-1122-2-2-11-22-111-1-1-1112i−2i2i−2i-11−ii−ii−ii−ii000000000000i3−i3i3−i3−33−3300000000
χ332-2-222-2-122-2-21-1122-2-2-11-22-111-1-1-111−2i2i−2i2i-11i−ii−ii−ii−i000000000000−i3i3−i3i3−33−3300000000
χ342-2-222-2-122-2-21-1122-2-2-11-22-111-1-1-111−2i2i−2i2i-11i−ii−ii−ii−i000000000000i3−i3i3−i33−33−300000000
χ352-2-22-2222-22-2-22-20000-22002-22-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000002-20000
χ362-2-22-2222-22-2-22-20000-22002-22-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i200000000000000-220000
χ372-2-22-2222-22-2-22-20000-22002-22-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i200000000000000-220000
χ382-2-22-2222-22-2-22-20000-22002-22-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000002-20000
χ392-2-22-222-22-22-22-222-2-2-222-2-22-2222-2-20000-22000000000000000002i−2i000002i−2i−2i2i00000000
χ402-2-22-222-22-22-22-222-2-2-222-2-22-2222-2-20000-2200000000000000000−2i2i00000−2i2i2i−2i00000000
χ412-2-22-222-22-22-22-2-2-222-22-22-22-22-2-22200002-200000000000000000000000000000000002-2
χ422-2-22-222-22-22-22-2-2-222-22-22-22-22-2-22200002-20000000000000000000000000000000000-22
χ432-2-22-22-1-22-221-1122-2-21-12-21-11-1-1-11100001-13−3−333−3−330000000002i−2i0−i3i3i3−i3−iii−i00000000
χ442-2-22-22-1-22-221-1122-2-21-12-21-11-1-1-11100001-13−3−333−3−33000000000−2i2i0i3−i3−i3i3i−i−ii00000000
χ452-2-22-22-1-22-221-1122-2-21-12-21-11-1-1-11100001-1−333−3−333−30000000002i−2i0i3−i3−i3i3−iii−i00000000
χ462-2-22-22-1-22-221-1122-2-21-12-21-11-1-1-11100001-1−333−3−333−3000000000−2i2i0−i3i3i3−i3i−i−ii00000000
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
χ514444-4-4-24-4-44-2-2-200002200-2-22200002222−22−2200−2−2−2−222220000000000000000000000000000
χ524444-4-4-24-4-44-2-2-200002200-2-2220000−22−222222002222−2−2−2−20000000000000000000000000000
χ534444-4-4-2-444-4-2-2-2-4-4-4-4224422-2-222220000-2-2000000000000000000000000000000000000
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
χ624-4-444-44-4-444-44-400004-400-444-40000000000000000000000000000000000000000000000
χ634-4-444-4-244-4-42-22-4-444-224-4-222-222-2-200002-2000000000000000000000000000000000000
χ644-4-444-4-2-4-4442-220000-22002-2-2200000000006−6−66−666−60000000000000000000000000000
χ654-4-444-4-2-4-4442-220000-22002-2-220000000000−666−66−6−660000000000000000000000000000
χ664-4-44-44-24-44-42-2200002-200-22-220000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ674-4-44-44-24-44-42-2200002-200-22-2200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ684-4-44-44-2-44-442-22-4-4442-2-442-22-222-2-20000-22000000000000000000000000000000000000
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.