Finite Group Databasebeta

← Group #10949040

Character table — Group #10949040

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888881212121212121212161616161616161616161616242424242424242424242424
order122222344446668888224466881212121224242424668812122424242424241616161616161616444412121212121212122244444416161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111
χ8111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111
χ91111-1-111-1-1111111111-11-1-1-1-1-11-1-1111111-11-11-1-1-111-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-1
χ101111-1-111-1-1111111111-11-1-1-1-1-11-1-1111111-11-11-1-1-111-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-11111-1-1
χ111111-1-111-1-1111111111-11-1-1-1-1-11-1-1111111-11-11-1-1-111-1-1-1-1-1-111111-11-111-1-111-1-1-1-111-1-111-1-111
χ121111-1-111-1-1111111111-11-1-1-1-1-11-1-1111111-11-11-1-1-111-1-1-1-1-1-11111-11-11-1-111-1-11111-1-111-1-1-1-111
χ131111-1-111-1-111111111-11-11-1-1-1-11-1-111111-11-11-11-1-1-1-1111111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-111-1-111
χ141111-1-111-1-111111111-11-11-1-1-1-11-1-111111-11-11-11-1-1-1-1111111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-111
χ151111-1-111-1-111111111-11-11-1-1-1-11-1-111111-11-11-11-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-111-1-1
χ161111-1-111-1-111111111-11-11-1-1-1-11-1-111111-11-11-11-1-1-1-111-1-1-1-11111-111-1-1-11111-1-111-1-1-1-11111-1-1
χ1722222222222222-2-2-2-2222222-2-22222-2-2-2-222-2-222-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ192222222-2-2-2-222200002-2-222200-2-2-2-200002-200-2200000022−2−222−2−2000000000000000000002−22−2
χ202222222-2-2-2-222200002-2-222200-2-2-2-200002-200-22000000−2−222−2−22200000000000000000000−22−22
χ212222222-2-2-2-22220000-222-22200-2-2-2-20000-22002-200000022−2−222−2−200000000000000000000−22−22
χ222222222-2-2-2-22220000-222-22200-2-2-2-20000-22002-2000000−2−222−2−222000000000000000000002−22−2
χ23222222-12222-1-1-122222222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-122222222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2-211111111000000000000
χ25222222-12222-1-1-12222-2-2-2-2-1-122-1-1-1-1-1-1-1-111-2-211-1-111110000000022-2-2-1-1-1-11111000000000000
χ26222222-12222-1-1-12222-2-2-2-2-1-122-1-1-1-1-1-1-1-111-2-211-1-1111100000000-2-2221111-1-1-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-22222-1-1-2-2-1-1-1-11111-1-1-2-2-1-1111111000000000000−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-12222-1-1-1-2-2-2-22222-1-1-2-2-1-1-1-11111-1-1-2-2-1-1111111000000000000i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-2-2-1-1-1-1111111221111-1-1-1-1000000000000−i3i3−i3i3i3−i3i3−i3000000000000
χ30222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-2-2-1-1-1-1111111221111-1-1-1-1000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ312222-2-222-2-22222-2-2-2-22-22-2-2-2222-2-22-2-2-2-22-2-222-222-2-22200000000000000000000000000000000
χ322222-2-222-2-22222-2-2-2-2-22-22-2-2222-2-22-2-2-2-2-222-2-222222-2-200000000000000000000000000000000
χ332222-2-22-222-2222000022-2-2-2-200-222-200002200-2-200000022−2−2−2−222000000000000000000002−2−22
χ342222-2-22-222-2222000022-2-2-2-200-222-200002200-2-2000000−2−22222−2−200000000000000000000−222−2
χ352222-2-22-222-22220000-2-222-2-200-222-20000-2-2002200000022−2−2−2−22200000000000000000000−222−2
χ362222-2-22-222-22220000-2-222-2-200-222-20000-2-20022000000−2−22222−2−2000000000000000000002−2−22
χ372222-2-2-12-2-22-1-1-122222-22-211-2-2-111-1-1-1-1-1-112-2-1111-1-111000000002-22-2-1-111-1-111000000000000
χ382222-2-2-12-2-22-1-1-122222-22-211-2-2-111-1-1-1-1-1-112-2-1111-1-11100000000-22-2211-1-111-1-1000000000000
χ392222-2-2-12-2-22-1-1-12222-22-2211-2-2-111-1-1-1-1-11-1-221-11111-1-1000000002-2-22-1-11111-1-1000000000000
χ402222-2-2-12-2-22-1-1-12222-22-2211-2-2-111-1-1-1-1-11-1-221-11111-1-100000000-222-211-1-1-1-111000000000000
χ412222-2-2-12-2-22-1-1-1-2-2-2-22-22-21122-111-11111-11-22-11-1-111-1-1000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ422222-2-2-12-2-22-1-1-1-2-2-2-22-22-21122-111-11111-11-22-11-1-111-1-1000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ432222-2-2-12-2-22-1-1-1-2-2-2-2-22-221122-111-111111-12-21-1-1-1-1-111000000000000−i3i3i3−i3i3−i3−i3i3000000000000
χ442222-2-2-12-2-22-1-1-1-2-2-2-2-22-221122-111-111111-12-21-1-1-1-1-111000000000000i3−i3−i3i3−i3i3i3−i3000000000000
χ452-2-222-22-22-22-2-2222-2-200002-22-2-22-2222-2-20000002-200000000000000000000000000002-22-20000
χ462-2-222-22-22-22-2-2222-2-200002-22-2-22-2222-2-20000002-20000000000000000000000000000-22-220000
χ472-2-222-22-22-22-2-22-2-22200002-2-22-22-22-2-222000000-220000000000000000000000002-22-200000000
χ482-2-222-22-22-22-2-22-2-22200002-2-22-22-22-2-222000000-22000000000000000000000000-22-2200000000
χ492-2-22-222-2-222-2-2222-2-20000-22-22-2-22222-2-2000000-2200000000000000000000000000002-2-220000
χ502-2-22-222-2-222-2-2222-2-20000-22-22-2-22222-2-2000000-220000000000000000000000000000-222-20000
χ512-2-22-222-2-222-2-22-2-2220000-222-2-2-222-2-2220000002-20000000000000000000000002-2-2200000000
χ522-2-22-222-2-222-2-22-2-2220000-222-2-2-222-2-2220000002-2000000000000000000000000-222-200000000
χ53444444-2-4-4-4-4-2-2-200004-4-44-2-20022220000-22002-200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-444-4-2-200222200002-200-2200000000000000000000000000000000000000
χ554444-4-4-2-444-4-2-2-2000044-4-422002-2-220000-2-2002200000000000000000000000000000000000000
χ564444-4-4-2-444-4-2-2-20000-4-44422002-2-2200002200-2-200000000000000000000000000000000000000
χ5744-4-400400004-4-422−2222−2200000000000022−2222−2200000000000000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47000000000000000000000000
χ5844-4-400400004-4-422−2222−2200000000000022−2222−220000000000000000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47000000000000000000000000
χ5944-4-400400004-4-4−2222−2222000000000000−2222−22220000000000000000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43000000000000000000000000
χ6044-4-400400004-4-4−2222−2222000000000000−2222−222200000000000000002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43000000000000000000000000
χ614-44-40040000-44-422−22−222200000000000022−22−22220000000000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000000000000000000000000000
χ624-44-40040000-44-422−22−222200000000000022−22−2222000000000000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000000000000000000000000000
χ634-44-40040000-44-4−222222−22000000000000−222222−22000000000000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000000000000000000000000000
χ644-44-40040000-44-4−222222−22000000000000−222222−220000000000002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000000000000000000000000000
χ654-4-444-444-44-4-4-44000000004-4004-44-4000000000000000000000000000000000000000000000000
χ664-4-444-4-24-44-422-200000000-2200-22-2200000000000023−2323−2300000000000000000000000000000000
χ674-4-444-4-24-44-422-200000000-2200-22-22000000000000−2323−232300000000000000000000000000000000
χ684-4-444-4-2-44-4422-244-4-40000-224-42-22-2-2-222000000-22000000000000000000000000000000000000
χ694-4-444-4-2-44-4422-2-4-4440000-22-442-22-222-2-20000002-2000000000000000000000000000000000000
χ704-4-44-44444-4-4-4-4400000000-440044-4-4000000000000000000000000000000000000000000000000
χ714-4-44-44-244-4-422-2000000002-200-2-22200000000000023−23−232300000000000000000000000000000000
χ724-4-44-44-244-4-422-2000000002-200-2-222000000000000−232323−2300000000000000000000000000000000
χ734-4-44-44-2-4-44422-244-4-400002-2-4422-2-2-2-2220000002-2000000000000000000000000000000000000
χ744-4-44-44-2-4-44422-2-4-44400002-24-422-2-222-2-2000000-22000000000000000000000000000000000000
χ7588-8-800-40000-44442−4242−42000000000000−2222−222200000000000000000000000000000000000000000000
χ7688-8-800-40000-444−4242−424200000000000022−2222−2200000000000000000000000000000000000000000000
χ778-88-800-400004-4442−42−4242000000000000−222222−2200000000000000000000000000000000000000000000
χ788-88-800-400004-44−424242−4200000000000022−22−222200000000000000000000000000000000000000000000

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