Finite Group Databasebeta

← Group #10949024

Character table — Group #10949024

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order1222223444466688882244666666881212121212121212242424242222224466666666666688121212122424242424241616161616161616161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ6111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111111111-1-1-1-111-1-1
χ8111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ91111-1-111-1-1111111111-11-1-1-111-1-1-1-11-1-111-1-11111111-1-111-1-11111-1-1-1-111111-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ101111-1-111-1-1111111111-11-1-1-111-1-1-1-11-1-111-1-11111111-1-111-1-11111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-11-11
χ111111-1-111-1-1111111111-11-1-1-111-1-1-1-11-1-111-1-111111-1-111-1-111-1-1-1-11111-1-1-1-11-11111-1-111-1-11111-1-1-1-111-1-1-11-11
χ121111-1-111-1-1111111111-11-1-1-111-1-1-1-11-1-111-1-111111-1-111-1-111-1-1-1-11111-1-1-1-11-11111-1-111-1-1-1-1-1-11111-1-1111-11-1
χ131111-1-111-1-111111111-11-11-1-1-1-111-1-11-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-111-111-1
χ141111-1-111-1-111111111-11-11-1-1-1-111-1-11-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1111111-1-11-1-11
χ151111-1-111-1-111111111-11-11-1-1-1-111-1-11-1-1-1-11111111-1-11111-1-1-1-1-1-111111111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ161111-1-111-1-111111111-11-11-1-1-1-111-1-11-1-1-1-11111111-1-11111-1-1-1-1-1-111111111-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-111-1
χ1722222222222222-2-2-2-22222222222-2-222222222-2-2-2-200000000000000000000-2-20000-2-2-2-2-2-20000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222-2-2-2-22-2-2-2-200000000000000000000220000-2-222220000000000000000
χ192222222-2-2-2-222200002-2-222222-2-200-2-2-2-2-222-200000000000000000000000000000000000022−2−222−2−22−22−20000
χ202222222-2-2-2-222200002-2-222222-2-200-2-2-2-2-222-2000000000000000000000000000000000000−2−222−2−222−22−220000
χ212222222-2-2-2-22220000-222-222-2-22200-2-2-222-2-2-200000000000000000000000000000000000022−2−222−2−2−22−220000
χ222222222-2-2-2-22220000-222-222-2-22200-2-2-222-2-2-2000000000000000000000000000000000000−2−222−2−2222−22−20000
χ23222222-12222-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000000000000000
χ24222222-12222-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111221111-1-1-1-1-1-10000000000000000
χ25222222-12222-1-1-12222-2-2-2-2-1-1111122-1-1-11111-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-11111-2-21111-1-111110000000000000000
χ26222222-12222-1-1-12222-2-2-2-2-1-1111122-1-1-11111-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-2-2-1-1-1-1-1-111110000000000000000
χ27222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-2-2−i3−i3i3i31111110000000000000000
χ28222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-2-2i3i3−i3−i31111110000000000000000
χ29222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-2-2-1-1-11111-1111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i322i3i3−i3−i311-1-1-1-10000000000000000
χ30222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-2-2-1-1-11111-1111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i322−i3−i3i3i311-1-1-1-10000000000000000
χ312222-2-222-2-22222-2-2-2-22-22-2-2-222-2-2222-2-222-2-22-2-2-2-200000000000000000000-22000022-2-2220000000000000000
χ322222-2-222-2-22222-2-2-2-2-22-22-2-2-2-222222-2-2-2-2222-2-2-2-2000000000000000000002-200002222-2-20000000000000000
χ332222-2-22-222-2222000022-2-2-2-2222200-222-2-2-2-2-200000000000000000000000000000000000022−2−2−2−2222−2−220000
χ342222-2-22-222-2222000022-2-2-2-2222200-222-2-2-2-2-2000000000000000000000000000000000000−2−22222−2−2−222−20000
χ352222-2-22-222-22220000-2-222-2-2-2-2-2-200-2222222-200000000000000000000000000000000000022−2−2−2−222−222−20000
χ362222-2-22-222-22220000-2-222-2-2-2-2-2-200-2222222-2000000000000000000000000000000000000−2−22222−2−22−2−220000
χ372222-2-2-12-2-22-1-1-122222-22-211-1-111-2-2-111-1-111-1-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-12-2111111-1-1110000000000000000
χ382222-2-2-12-2-22-1-1-122222-22-211-1-111-2-2-111-1-111-1-1-1-1-1-2-222-2-2221111-1-1-1-111112-2-1-1-1-111-1-1110000000000000000
χ392222-2-2-12-2-22-1-1-12222-22-221111-1-1-2-2-11111-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-22-1-1-1-11111-1-10000000000000000
χ402222-2-2-12-2-22-1-1-12222-22-221111-1-1-2-2-11111-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-1-2211111111-1-10000000000000000
χ412222-2-2-12-2-22-1-1-1-2-2-2-22-22-211-1-11122-111-1-111-1111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-22i3i3−i3−i3-1-111-1-10000000000000000
χ422222-2-2-12-2-22-1-1-1-2-2-2-22-22-211-1-11122-111-1-111-1111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-22−i3−i3i3i3-1-111-1-10000000000000000
χ432222-2-2-12-2-22-1-1-1-2-2-2-2-22-221111-1-122-11111-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32-2−i3−i3i3i3-1-1-1-1110000000000000000
χ442222-2-2-12-2-22-1-1-1-2-2-2-2-22-221111-1-122-11111-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i32-2i3i3−i3−i3-1-1-1-1110000000000000000
χ452-2-222-22-22-22-2-2222-2-200002-200002-2-22-20000222-2-200002-22-2000000002-22-2002-22-22-200000000000000000000
χ462-2-222-22-22-22-2-2222-2-200002-200002-2-22-20000222-2-20000-22-2200000000-22-2200-22-222-200000000000000000000
χ472-2-222-22-22-22-2-22-2-22200002-20000-22-22-200002-2-2222-22-200002-22-22-22-20000000000-2200000000000000000000
χ482-2-222-22-22-22-2-22-2-22200002-20000-22-22-200002-2-222-22-220000-22-22-22-220000000000-2200000000000000000000
χ492-2-222-2-1-22-2211-122-2-20000-11−i3i3−i3i32-21-11−i3i3−i3i3-1-1-11100002-22-2−i3i3i3−i3−i3i3i3−i3-11-1100-11-11-11−i3i3−i3i30000000000000000
χ502-2-222-2-1-22-2211-122-2-20000-11−i3i3−i3i32-21-11−i3i3−i3i3-1-1-1110000-22-22i3−i3−i3i3i3−i3−i3i31-11-1001-11-1-11−i3i3−i3i30000000000000000
χ512-2-222-2-1-22-2211-122-2-20000-11i3−i3i3−i32-21-11i3−i3i3−i3-1-1-11100002-22-2i3−i3−i3i3i3−i3−i3i3-11-1100-11-11-11i3−i3i3−i30000000000000000
χ522-2-222-2-1-22-2211-122-2-20000-11i3−i3i3−i32-21-11i3−i3i3−i3-1-1-1110000-22-22−i3i3i3−i3−i3i3i3−i31-11-1001-11-1-11i3−i3i3−i30000000000000000
χ532-2-222-2-1-22-2211-1-2-2220000-11−i3i3−i3i3-221-11−i3i3−i3i3-111-1-12-22-20000-11-11-11-11−i3i3i3−i300−i3i3i3−i31-1i3−i3i3−i30000000000000000
χ542-2-222-2-1-22-2211-1-2-2220000-11−i3i3−i3i3-221-11−i3i3−i3i3-111-1-1-22-2200001-11-11-11-1i3−i3−i3i300i3−i3−i3i31-1i3−i3i3−i30000000000000000
χ552-2-222-2-1-22-2211-1-2-2220000-11i3−i3i3−i3-221-11i3−i3i3−i3-111-1-12-22-20000-11-11-11-11i3−i3−i3i300i3−i3−i3i31-1−i3i3−i3i30000000000000000
χ562-2-222-2-1-22-2211-1-2-2220000-11i3−i3i3−i3-221-11i3−i3i3−i3-111-1-1-22-2200001-11-11-11-1−i3i3i3−i300−i3i3i3−i31-1−i3i3−i3i30000000000000000
χ572-2-22-222-2-222-2-2222-2-20000-220000-22-2-220000222-2-200002-2-22000000002-22-200-22-22-2200000000000000000000
χ582-2-22-222-2-222-2-2222-2-20000-220000-22-2-220000222-2-20000-222-200000000-22-22002-22-2-2200000000000000000000
χ592-2-22-222-2-222-2-22-2-2220000-2200002-2-2-2200002-2-2222-2-2200002-22-2-22-2200000000002-200000000000000000000
χ602-2-22-222-2-222-2-22-2-2220000-2200002-2-2-2200002-2-222-222-20000-22-222-22-200000000002-200000000000000000000
χ612-2-22-22-1-2-22211-122-2-200001-1−i3i3i3−i3-2211-1−i3i3i3−i3-1-1-11100002-2-22−i3i3i3−i3i3−i3−i3i3-11-11001-11-11-1−i3i3i3−i30000000000000000
χ622-2-22-22-1-2-22211-122-2-200001-1−i3i3i3−i3-2211-1−i3i3i3−i3-1-1-1110000-222-2i3−i3−i3i3−i3i3i3−i31-11-100-11-111-1−i3i3i3−i30000000000000000
χ632-2-22-22-1-2-22211-122-2-200001-1i3−i3−i3i3-2211-1i3−i3−i3i3-1-1-11100002-2-22i3−i3−i3i3−i3i3i3−i3-11-11001-11-11-1i3−i3−i3i30000000000000000
χ642-2-22-22-1-2-22211-122-2-200001-1i3−i3−i3i3-2211-1i3−i3−i3i3-1-1-1110000-222-2−i3i3i3−i3i3−i3−i3i31-11-100-11-111-1i3−i3−i3i30000000000000000
χ652-2-22-22-1-2-22211-1-2-22200001-1−i3i3i3−i32-211-1−i3i3i3−i3-111-1-12-2-220000-11-111-11-1−i3i3i3−i300i3−i3−i3i3-11i3−i3−i3i30000000000000000
χ662-2-22-22-1-2-22211-1-2-22200001-1−i3i3i3−i32-211-1−i3i3i3−i3-111-1-1-222-200001-11-1-11-11i3−i3−i3i300−i3i3i3−i3-11i3−i3−i3i30000000000000000
χ672-2-22-22-1-2-22211-1-2-22200001-1i3−i3−i3i32-211-1i3−i3−i3i3-111-1-12-2-220000-11-111-11-1i3−i3−i3i300−i3i3i3−i3-11−i3i3i3−i30000000000000000
χ682-2-22-22-1-2-22211-1-2-22200001-1i3−i3−i3i32-211-1i3−i3−i3i3-111-1-1-222-200001-11-1-11-11−i3i3i3−i300i3−i3−i3i3-11−i3i3i3−i30000000000000000
χ69444444-2-4-4-4-4-2-2-200004-4-44-2-2-2-2220022222-2-220000000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-20000-444-4-2-222-2-200222-2-22220000000000000000000000000000000000000000000000000000
χ714444-4-4-2-444-4-2-2-2000044-4-422-2-2-2-2002-2-2222220000000000000000000000000000000000000000000000000000
χ724444-4-4-2-444-4-2-2-20000-4-444222222002-2-2-2-2-2-220000000000000000000000000000000000000000000000000000
χ7344-4-400400004-4-422−2222−220000000000000000000022−2222−220000000000000000000000000000000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ4700000000
χ7444-4-400400004-4-422−2222−220000000000000000000022−2222−22000000000000000000000000000000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ4700000000
χ7544-4-400400004-4-4−2222−222200000000000000000000−2222−2222000000000000000000000000000000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4300000000
χ7644-4-400400004-4-4−2222−222200000000000000000000−2222−22220000000000000000000000000000000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ4300000000
χ774-44-40040000-44-422−22−22220000000000000000000022−22−222200000000000000000000000000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43000000000000
χ784-44-40040000-44-422−22−22220000000000000000000022−22−2222000000000000000000000000000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43000000000000
χ794-44-40040000-44-4−222222−2200000000000000000000−222222−22000000000000000000000000000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47000000000000
χ804-44-40040000-44-4−222222−2200000000000000000000−222222−2200000000000000000000000000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47000000000000
χ814-4-444-444-44-4-4-44000000004-40000004-440000-40000000000000000000000000000000000000000000000000000
χ824-4-444-4-24-44-422-200000000-22−2i32i32i3−2i300-22-22i3−2i3−2i32i320000000000000000000000000000000000000000000000000000
χ834-4-444-4-24-44-422-200000000-222i3−2i3−2i32i300-22-2−2i32i32i3−2i320000000000000000000000000000000000000000000000000000
χ844-4-44-44444-4-4-4-4400000000-4400000044-40000-40000000000000000000000000000000000000000000000000000
χ854-4-44-44-244-4-422-2000000002-2−2i32i3−2i32i300-2-222i3−2i32i3−2i320000000000000000000000000000000000000000000000000000
χ864-4-44-44-244-4-422-2000000002-22i3−2i32i3−2i300-2-22−2i32i3−2i32i320000000000000000000000000000000000000000000000000000
χ8788-8-800-40000-44442−4242−4200000000000000000000−2222−2222000000000000000000000000000000000000000000000000
χ8888-8-800-40000-444−4242−42420000000000000000000022−2222−22000000000000000000000000000000000000000000000000
χ898-88-800-400004-4442−42−424200000000000000000000−222222−22000000000000000000000000000000000000000000000000
χ908-88-800-400004-44−424242−420000000000000000000022−22−2222000000000000000000000000000000000000000000000000

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