Finite Group Databasebeta

← Group #10691178

Character table — Group #10691178

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order1222223444466612121212224444446612121212121212121212246666888888881212121224242424242424242424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-111-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11-1-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11-1-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111-1-1-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11-1-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111-1-1-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11-1-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-222-2-222-2-2-2-222-2-2-2-2-2-222-2-200000000-2-2220000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-222-2-2220000000022-2-20000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-2-2-2-2-222222-2222200000000-2-2-2-20000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-22-2-2-2-20000000022220000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-11111-1-11111-2-2-1-1110000000011-1-133−3−333−3−333−3−333−3−3000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-11111-1-11111-2-2-1-1110000000011-1-1−3−333−3−333−3−333−3−333000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-111111111000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-111112211-1-100000000-1-11133−3−333−3−3−3−333−3−333000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-111112211-1-100000000-1-111−3−333−3−33333−3−333−3−3000000000000
χ29222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-22-1-1112i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ30222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-22-1-111−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1111111-1-1-1-12-2-1-1-1-1000000001111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1111111-1-1-1-12-2-1-1-1-1000000001111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-1-1-1-1-11111112-211-1-12i2i−2i−2i−2i−2i2i2i11-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-1-1-1-1-11111112-211-1-1−2i−2i2i2i2i2i−2i−2i11-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-22111100000000-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-22111100000000-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ372222-2-2222-2-22222222002-2002-2-2-222-2-2-2-222-2-2000000000000000000000000000000000000002i−2i2i−2i0000
χ382222-2-2222-2-22222222002-2002-2-2-222-2-2-2-222-2-200000000000000000000000000000000000000−2i2i−2i2i0000
χ392222-2-2222-2-2222222200-2200-22-2-2-2-222-2-2-2-22200000000000000000000000000000000002i−2i2i−2i00000000
χ402222-2-2222-2-2222222200-2200-22-2-2-2-222-2-2-2-2220000000000000000000000000000000000−2i2i−2i2i00000000
χ412222-2-22-2-222222-2-2-2-2002-200-22-2-222-2-222-2-222000000000000000000000000000000000000002-2-220000
χ422222-2-22-2-222222-2-2-2-2002-200-22-2-222-2-222-2-22200000000000000000000000000000000000000-222-20000
χ432222-2-22-2-222222-2-2-2-200-22002-2-2-2-2-2222222-2-200000000000000000000000000000000002-2-2200000000
χ442222-2-22-2-222222-2-2-2-200-22002-2-2-2-2-2222222-2-20000000000000000000000000000000000-222-200000000
χ452-22-22-222i−2i2i−2i2-2-22i2i−2i−2i2-2002i−2i002-200002i−2i0000002-2001+i−1−i1−i−1+i1+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ462-22-22-222i−2i2i−2i2-2-22i2i−2i−2i2-2002i−2i002-200002i−2i0000002-200−1−i1+i−1+i1−i−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ472-22-22-222i−2i2i−2i2-2-22i2i−2i−2i-2200−2i2i002-200002i−2i000000-22001+i−1−i1−i−1+i−1−i1+i−1+i1−i00−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ482-22-22-222i−2i2i−2i2-2-22i2i−2i−2i-2200−2i2i002-200002i−2i000000-2200−1−i1+i−1+i1−i1+i−1−i1−i−1+i00−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ492-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i2-200−2i2i002-20000−2i2i0000002-2001−i−1+i1+i−1−i1−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ502-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i2-200−2i2i002-20000−2i2i0000002-200−1+i1−i−1−i1+i−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ512-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i-22002i−2i002-20000−2i2i000000-22001−i−1+i1+i−1−i−1+i1−i−1−i1+i002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ522-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i-22002i−2i002-20000−2i2i000000-2200−1+i1−i−1−i1+i1−i−1+i1+i−1−i002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ532-22-22-2-12i−2i2i−2i-111−i−iii2-2002i−2i00-113−33−3−ii−i3i3−i3i300-11−i3i31+i−1−i1−i−1+i1+i−1−i1−i−1+i3−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ542-22-22-2-12i−2i2i−2i-111−i−iii2-2002i−2i00-113−33−3−ii−i3i3−i3i300-11−i3i3−1−i1+i−1+i1−i−1−i1+i−1+i1−i3−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ552-22-22-2-12i−2i2i−2i-111−i−iii2-2002i−2i00-11−33−33−iii3−i3i3−i300-11i3−i31+i−1−i1−i−1+i1+i−1−i1−i−1+i−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ562-22-22-2-12i−2i2i−2i-111−i−iii2-2002i−2i00-11−33−33−iii3−i3i3−i300-11i3−i3−1−i1+i−1+i1−i−1−i1+i−1+i1−i−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ572-22-22-2-12i−2i2i−2i-111−i−iii-2200−2i2i00-113−33−3−ii−i3i3−i3i3001-1i3−i31+i−1−i1−i−1+i−1−i1+i−1+i1−i−33i−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ582-22-22-2-12i−2i2i−2i-111−i−iii-2200−2i2i00-113−33−3−ii−i3i3−i3i3001-1i3−i3−1−i1+i−1+i1−i1+i−1−i1−i−1+i−33i−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ592-22-22-2-12i−2i2i−2i-111−i−iii-2200−2i2i00-11−33−33−iii3−i3i3−i3001-1−i3i31+i−1−i1−i−1+i−1−i1+i−1+i1−i3−3i−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ602-22-22-2-12i−2i2i−2i-111−i−iii-2200−2i2i00-11−33−33−iii3−i3i3−i3001-1−i3i3−1−i1+i−1+i1−i1+i−1−i1−i−1+i3−3i−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ612-22-22-2-1−2i2i−2i2i-111ii−i−i2-200−2i2i00-113−33−3i−ii3−i3i3−i300-11i3−i31−i−1+i1+i−1−i1−i−1+i1+i−1−i3−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ622-22-22-2-1−2i2i−2i2i-111ii−i−i2-200−2i2i00-113−33−3i−ii3−i3i3−i300-11i3−i3−1+i1−i−1−i1+i−1+i1−i−1−i1+i3−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ632-22-22-2-1−2i2i−2i2i-111ii−i−i2-200−2i2i00-11−33−33i−i−i3i3−i3i300-11−i3i31−i−1+i1+i−1−i1−i−1+i1+i−1−i−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ642-22-22-2-1−2i2i−2i2i-111ii−i−i2-200−2i2i00-11−33−33i−i−i3i3−i3i300-11−i3i3−1+i1−i−1−i1+i−1+i1−i−1−i1+i−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ652-22-22-2-1−2i2i−2i2i-111ii−i−i-22002i−2i00-113−33−3i−ii3−i3i3−i3001-1−i3i31−i−1+i1+i−1−i−1+i1−i−1−i1+i−33−ii−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ662-22-22-2-1−2i2i−2i2i-111ii−i−i-22002i−2i00-113−33−3i−ii3−i3i3−i3001-1−i3i3−1+i1−i−1−i1+i1−i−1+i1+i−1−i−33−iiζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ672-22-22-2-1−2i2i−2i2i-111ii−i−i-22002i−2i00-11−33−33i−i−i3i3−i3i3001-1i3−i31−i−1+i1+i−1−i−1+i1−i−1−i1+i3−3−ii−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ682-22-22-2-1−2i2i−2i2i-111ii−i−i-22002i−2i00-11−33−33i−i−i3i3−i3i3001-1i3−i3−1+i1−i−1−i1+i1−i−1+i1+i−1−i3−3−iiζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ694444-4-4-244-4-4-2-2-2-2-2-2-2004-4004-422-2-22222-2-2220000000000000000000000000000000000000000000000
χ704444-4-4-244-4-4-2-2-2-2-2-2-200-4400-442222-2-22222-2-20000000000000000000000000000000000000000000000
χ714444-4-4-2-4-444-2-2-22222004-400-4422-2-222-2-222-2-20000000000000000000000000000000000000000000000
χ724444-4-4-2-4-444-2-2-2222200-44004-42222-2-2-2-2-2-2220000000000000000000000000000000000000000000000
χ734-44-4-4444i−4i−4i4i4-4-44i4i−4i−4i00000000-440000−4i4i00000000000000000000000000000000000000000000000000
χ744-44-4-444−4i4i4i−4i4-4-4−4i−4i4i4i00000000-4400004i−4i00000000000000000000000000000000000000000000000000
χ754-44-4-44-24i−4i−4i4i-222−2i−2i2i2i000000002-223−23−23232i−2i−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ764-44-4-44-24i−4i−4i4i-222−2i−2i2i2i000000002-2−232323−232i−2i2i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ774-44-4-44-2−4i4i4i−4i-2222i2i−2i−2i000000002-223−23−2323−2i2i2i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ784-44-4-44-2−4i4i4i−4i-2222i2i−2i−2i000000002-2−232323−23−2i2i−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-4−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-44i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000

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