Finite Group Databasebeta

← Group #10691183

Character table — Group #10691183

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order12222234444666121212124444444466121212121212121212124488888888121212121212121224242424242424242424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222222222-2-22222-2-22222-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22200000000-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-2-2-222-2-22222-2-2-2-2-2-222222-20000000022-2-2-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2200000000-2-22222-2-20000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-111111111-2-200000000-1-111-1-11133−3−333−3−333−3−333−3−3000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-111111111-2-200000000-1-111-1-111−3−333−3−333−3−333−3−333000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111220000000011-1-111-1-133−3−333−3−3−3−333−3−333000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111220000000011-1-111-1-1−3−333−3−33333−3−333−3−3000000000000
χ29222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-111-1-1-1-11111-222i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ30222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-111-1-1-1-11111-22−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-111-1-1-1-111112-22i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-111-1-1-1-111112-2−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1111111-1-1-1-12-200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1111111-1-1-1-12-200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-220000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-220000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ372222-2-2222-2-222222222-200002-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000002i−2i2i−2i0000
χ382222-2-2222-2-222222222-200002-2-2-2-2-222-2-222-2-200000000000000000000000000000000000000−2i2i−2i2i0000
χ392222-2-2222-2-22222222-220000-22-2-2-2-2-2-222-2-22200000000000000000000000000000000002i−2i2i−2i00000000
χ402222-2-2222-2-22222222-220000-22-2-2-2-2-2-222-2-2220000000000000000000000000000000000−2i2i−2i2i00000000
χ412222-2-22-2-222222-2-2-2-22-20000-22-2-22222-2-2-2-222000000000000000000000000000000000000002-2-220000
χ422222-2-22-2-222222-2-2-2-22-20000-22-2-22222-2-2-2-22200000000000000000000000000000000000000-222-20000
χ432222-2-22-2-222222-2-2-2-2-2200002-2-2-222-2-22222-2-200000000000000000000000000000000002-2-2200000000
χ442222-2-22-2-222222-2-2-2-2-2200002-2-2-222-2-22222-2-20000000000000000000000000000000000-222-200000000
χ452-2-222-222i−2i2i−2i-22-22i2i−2i−2i002i−2i2-2002-22i−2i00000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i2i−2i002-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ462-2-222-222i−2i2i−2i-22-22i2i−2i−2i002i−2i2-2002-22i−2i0000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i2i−2i002-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ472-2-222-222i−2i2i−2i-22-22i2i−2i−2i00−2i2i-22002-22i−2i00000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i−2i2i00-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ482-2-222-222i−2i2i−2i-22-22i2i−2i−2i00−2i2i-22002-22i−2i0000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i−2i2i00-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ492-2-222-22−2i2i−2i2i-22-2−2i−2i2i2i002i−2i-22002-2−2i2i00000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i2i−2i00-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ502-2-222-22−2i2i−2i2i-22-2−2i−2i2i2i002i−2i-22002-2−2i2i0000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i2i−2i00-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ512-2-222-22−2i2i−2i2i-22-2−2i−2i2i2i00−2i2i2-2002-2−2i2i00000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i−2i2i002-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ522-2-222-22−2i2i−2i2i-22-2−2i−2i2i2i00−2i2i2-2002-2−2i2i0000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i−2i2i002-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ532-2-222-2-12i−2i2i−2i1-11−i−iii002i−2i2-200-11−ii3−33−3−i3i3−i3i3001+i−1−i1−i−1+i1−i−1+i1+i−1−i−ii−i3i3-113−3−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ542-2-222-2-12i−2i2i−2i1-11−i−iii002i−2i2-200-11−ii3−33−3−i3i3−i3i300−1−i1+i−1+i1−i−1+i1−i−1−i1+i−ii−i3i3-113−3ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ552-2-222-2-12i−2i2i−2i1-11−i−iii002i−2i2-200-11−ii−33−33i3−i3i3−i3001+i−1−i1−i−1+i1−i−1+i1+i−1−i−iii3−i3-11−33−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ562-2-222-2-12i−2i2i−2i1-11−i−iii002i−2i2-200-11−ii−33−33i3−i3i3−i300−1−i1+i−1+i1−i−1+i1−i−1−i1+i−iii3−i3-11−33ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ572-2-222-2-12i−2i2i−2i1-11−i−iii00−2i2i-2200-11−ii3−33−3−i3i3−i3i3001+i−1−i1−i−1+i−1+i1−i−1−i1+ii−ii3−i31-1−33−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ582-2-222-2-12i−2i2i−2i1-11−i−iii00−2i2i-2200-11−ii3−33−3−i3i3−i3i300−1−i1+i−1+i1−i1−i−1+i1+i−1−ii−ii3−i31-1−33ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ592-2-222-2-12i−2i2i−2i1-11−i−iii00−2i2i-2200-11−ii−33−33i3−i3i3−i3001+i−1−i1−i−1+i−1+i1−i−1−i1+ii−i−i3i31-13−3−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ602-2-222-2-12i−2i2i−2i1-11−i−iii00−2i2i-2200-11−ii−33−33i3−i3i3−i300−1−i1+i−1+i1−i1−i−1+i1+i−1−ii−i−i3i31-13−3ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ612-2-222-2-1−2i2i−2i2i1-11ii−i−i002i−2i-2200-11i−i3−33−3i3−i3i3−i3001−i−1+i1+i−1−i−1−i1+i−1+i1−i−ii−i3i31-1−33−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ622-2-222-2-1−2i2i−2i2i1-11ii−i−i002i−2i-2200-11i−i3−33−3i3−i3i3−i300−1+i1−i−1−i1+i1+i−1−i1−i−1+i−ii−i3i31-1−33ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ632-2-222-2-1−2i2i−2i2i1-11ii−i−i002i−2i-2200-11i−i−33−33−i3i3−i3i3001−i−1+i1+i−1−i−1−i1+i−1+i1−i−iii3−i31-13−3−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ642-2-222-2-1−2i2i−2i2i1-11ii−i−i002i−2i-2200-11i−i−33−33−i3i3−i3i300−1+i1−i−1−i1+i1+i−1−i1−i−1+i−iii3−i31-13−3ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ652-2-222-2-1−2i2i−2i2i1-11ii−i−i00−2i2i2-200-11i−i3−33−3i3−i3i3−i3001−i−1+i1+i−1−i1+i−1−i1−i−1+ii−ii3−i3-113−3−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ662-2-222-2-1−2i2i−2i2i1-11ii−i−i00−2i2i2-200-11i−i3−33−3i3−i3i3−i300−1+i1−i−1−i1+i−1−i1+i−1+i1−ii−ii3−i3-113−3ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ672-2-222-2-1−2i2i−2i2i1-11ii−i−i00−2i2i2-200-11i−i−33−33−i3i3−i3i3001−i−1+i1+i−1−i1+i−1−i1−i−1+ii−i−i3i3-11−33−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ682-2-222-2-1−2i2i−2i2i1-11ii−i−i00−2i2i2-200-11i−i−33−33−i3i3−i3i300−1+i1−i−1−i1+i−1−i1+i−1+i1−ii−i−i3i3-11−33ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ694444-4-4-244-4-4-2-2-2-2-2-2-24-400004-42222-2-222-2-2220000000000000000000000000000000000000000000000
χ704444-4-4-244-4-4-2-2-2-2-2-2-2-440000-44222222-2-222-2-20000000000000000000000000000000000000000000000
χ714444-4-4-2-4-444-2-2-222224-40000-4422-2-2-2-22222-2-20000000000000000000000000000000000000000000000
χ724444-4-4-2-4-444-2-2-22222-4400004-422-2-222-2-2-2-2220000000000000000000000000000000000000000000000
χ734-4-44-4444i−4i−4i4i-44-44i4i−4i−4i00000000-44−4i4i000000000000000000000000000000000000000000000000000000
χ744-4-44-444−4i4i4i−4i-44-4−4i−4i4i4i00000000-444i−4i000000000000000000000000000000000000000000000000000000
χ754-4-44-44-24i−4i−4i4i2-22−2i−2i2i2i000000002-22i−2i23−23−2323−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ764-4-44-44-24i−4i−4i4i2-22−2i−2i2i2i000000002-22i−2i−232323−232i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ774-4-44-44-2−4i4i4i−4i2-222i2i−2i−2i000000002-2−2i2i23−23−23232i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ784-4-44-44-2−4i4i4i−4i2-222i2i−2i−2i000000002-2−2i2i−232323−23−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7988-8-80080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-4000044-443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-4000044-4−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-88-800800008-8-80000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-800-40000-444−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-40000-4444i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.