Finite Group Databasebeta

← Group #10711556

Character table — Group #10711556

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12448888222344468888881212242424246661212122424242424244488121212121616161616161616242424244848484848484848484848484848484816161616161616164444888816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111
χ91111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111ii−i−i
χ101111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iii
χ111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i
χ121111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111−i−iii
χ131111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iii
χ141111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−i
χ151111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii
χ161111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i
χ1722222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000000000000000
χ1922222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000000000000000
χ21222222222-2-222-2-22-2-2-2-222222222-2-22-2-2222-2-2-2-22-22-222-2-20000000022-2-2000000000000000000000000000000000000
χ22222222222-2-222-2-22-2-2-2-222222222-2-22-2-2222-2-2-2-2-22-22-2-22200000000-2-222000000000000000000000000000000000000
χ23222222222-2-2-12-2-2-1-2-2-2-222-1-1-1-1-1-111-111-1-1-111112-22-2-1-11100000000-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ24222222222-2-2-12-2-2-1-2-2-2-222-1-1-1-1-1-111-111-1-1-111112-22-2-1-11100000000-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ25222222222-2-2-12-2-2-1-2-2-2-222-1-1-1-1-1-111-111-1-1-11111-22-2211-1-10000000011-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ26222222222-2-2-12-2-2-1-2-2-2-222-1-1-1-1-1-111-111-1-1-11111-22-2211-1-10000000011-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2722222222-22-22-22-2222-2-2-2-22222222-2-22-2-2-2-222-2-200000000000000000000000000000000000000000000002i−2i002i−2i0000
χ2822222222-22-22-22-2222-2-2-2-22222222-2-22-2-2-2-222-2-20000000000000000000000000000000000000000000000−2i2i00−2i2i0000
χ2922222222-2-222-2-222-2-222-2-2222222-22-2-22-2-2-2-2-222000000000000000000000000000000000000000000002i−2i002i−2i000000
χ3022222222-2-222-2-222-2-222-2-2222222-22-2-22-2-2-2-2-22200000000000000000000000000000000000000000000−2i2i00−2i2i000000
χ312222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-111111122-2-2-1-1-1-12i2i−2i−2i2i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ322222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-111111122-2-2-1-1-1-1−2i−2i2i2i−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ332222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-1111111-2-22211112i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ342222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-1111111-2-2221111−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ352222-2-2-2-22-2-222-2-222222-2-222-2-2-2-2-2-22-2-22-2-222222-2-2222-2-200000000-2-222000000000000000000000000000000000000
χ362222-2-2-2-22-2-222-2-222222-2-222-2-2-2-2-2-22-2-22-2-22222-222-2-2-2220000000022-2-2000000000000000000000000000000000000
χ372222-2-2-2-22-2-2-12-2-2-12222-2-2-1-1111111-111-111-1-1-1-12-2-22-1-1110000000011-1-133−3−3−3−33333−3−3−3−33300000000000000000000
χ382222-2-2-2-22-2-2-12-2-2-12222-2-2-1-1111111-111-111-1-1-1-12-2-22-1-1110000000011-1-1−3−33333−3−3−3−33333−3−300000000000000000000
χ392222-2-2-2-22-2-2-12-2-2-12222-2-2-1-1111111-111-111-1-1-1-1-222-211-1-100000000-1-11133−3−3−3−333−3−33333−3−300000000000000000000
χ402222-2-2-2-22-2-2-12-2-2-12222-2-2-1-1111111-111-111-1-1-1-1-222-211-1-100000000-1-111−3−33333−3−333−3−3−3−33300000000000000000000
χ412222-2-2-2-2-22-22-22-22-2-2222222-2-2-2-22-2-22-2-222-2-22200000000000000000000000000000000000000000000002i−2i00−2i2i0000
χ422222-2-2-2-2-22-22-22-22-2-2222222-2-2-2-22-2-22-2-222-2-2220000000000000000000000000000000000000000000000−2i2i002i−2i0000
χ432222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-2-22-2-22-22222-2-2000000000000000000000000000000000000000000002i−2i00−2i2i000000
χ442222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-2-22-2-22-22222-2-200000000000000000000000000000000000000000000−2i2i002i−2i000000
χ4522-2-22i2i−2i−2i2222-2-2-222i−2i2i−2i2i−2i-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46
χ4622-2-22i2i−2i−2i2222-2-2-222i−2i2i−2i2i−2i-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46
χ4722-2-22i2i−2i−2i2-2-22-2222−2i2i−2i2i2i−2i-2-22i2i−2i−2i-2-2222-22i−2i−2i2i−2i2i000000000000000000000000000000000000−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ262ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ46000000000000
χ4822-2-22i2i−2i−2i2-2-22-2222−2i2i−2i2i2i−2i-2-22i2i−2i−2i-2-2222-22i−2i−2i2i−2i2i0000000000000000000000000000000000002ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ26−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46000000000000
χ4922-2-22i2i−2i−2i-22-222-2222i−2i−2i2i−2i2i-2-22i2i−2i−2i2-2-2-222−2i2i2i−2i−2i2i000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26000000002ζ14+2ζ46−2ζ14−2ζ462ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26−2ζ10−2ζ262ζ10+2ζ260000000000000000000000000000
χ5022-2-22i2i−2i−2i-22-222-2222i−2i−2i2i−2i2i-2-22i2i−2i−2i2-2-2-222−2i2i2i−2i−2i2i00000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600000000−2ζ14−2ζ462ζ14+2ζ46−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ262ζ10+2ζ26−2ζ10−2ζ260000000000000000000000000000
χ5122-2-22i2i−2i−2i-22-2-12-22-12i−2i−2i2i−2i2i11−i−iii-1111-1-1i−i−iii−i00003−33−32ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000−i3i3−i3i3−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10−ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ26−ζ14+ζ46ζ14−ζ46−ζ14+ζ46ζ14−ζ4600000000000000000000
χ5222-2-22i2i−2i−2i-22-2-12-22-12i−2i−2i2i−2i2i11−i−iii-1111-1-1i−i−iii−i00003−33−3−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000−i3i3−i3i3ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ26ζ10−ζ26ζ14−ζ46−ζ14+ζ46ζ14−ζ46−ζ14+ζ4600000000000000000000
χ5322-2-22i2i−2i−2i-22-2-12-22-12i−2i−2i2i−2i2i11−i−iii-1111-1-1i−i−iii−i0000−33−332ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000i3−i3i3−i3−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ26ζ10−ζ26ζ14−ζ46−ζ14+ζ46ζ14−ζ46−ζ14+ζ4600000000000000000000
χ5422-2-22i2i−2i−2i-22-2-12-22-12i−2i−2i2i−2i2i11−i−iii-1111-1-1i−i−iii−i0000−33−33−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000i3−i3i3−i3ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26ζ10−ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ26−ζ14+ζ46ζ14−ζ46−ζ14+ζ46ζ14−ζ4600000000000000000000
χ5522-2-22i2i−2i−2i-2-22222-22−2i2i2i−2i−2i2i-2-22i2i−2i−2i-22-22-22−2i2i−2i2i2i−2i000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000000000000−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ4600000000000000000000
χ5622-2-22i2i−2i−2i-2-22222-22−2i2i2i−2i−2i2i-2-22i2i−2i−2i-22-22-22−2i2i−2i2i2i−2i0000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ460000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ4600000000000000000000
χ5722-2-22i2i−2i−2i-2-22-122-2-1−2i2i2i−2i−2i2i11−i−iii1-11-11-1i−ii−i−ii00003−3−330000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46−i3i3i3−i3ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ4600000000000000000000
χ5822-2-22i2i−2i−2i-2-22-122-2-1−2i2i2i−2i−2i2i11−i−iii1-11-11-1i−ii−i−ii00003−3−3300002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46−i3i3i3−i3−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ4600000000000000000000
χ5922-2-22i2i−2i−2i-2-22-122-2-1−2i2i2i−2i−2i2i11−i−iii1-11-11-1i−ii−i−ii0000−333−30000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46i3−i3−i3i3−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ4600000000000000000000
χ6022-2-22i2i−2i−2i-2-22-122-2-1−2i2i2i−2i−2i2i11−i−iii1-11-11-1i−ii−i−ii0000−333−300002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46i3−i3−i3i3ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ4600000000000000000000
χ6122-2-2−2i−2i2i2i2222-2-2-22−2i2i−2i2i−2i2i-2-2−2i−2i2i2i222-2-2-2−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26
χ6222-2-2−2i−2i2i2i2222-2-2-22−2i2i−2i2i−2i2i-2-2−2i−2i2i2i222-2-2-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ26
χ6322-2-2−2i−2i2i2i2-2-22-22222i−2i2i−2i−2i2i-2-2−2i−2i2i2i-2-2222-2−2i2i2i−2i2i−2i0000000000000000000000000000000000002ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ46−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26000000000000
χ6422-2-2−2i−2i2i2i2-2-22-22222i−2i2i−2i−2i2i-2-2−2i−2i2i2i-2-2222-2−2i2i2i−2i2i−2i000000000000000000000000000000000000−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ462ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ26000000000000
χ6522-2-2−2i−2i2i2i-22-222-222−2i2i2i−2i2i−2i-2-2−2i−2i2i2i2-2-2-2222i−2i−2i2i2i−2i00000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600000000−2ζ10−2ζ262ζ10+2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ462ζ14+2ζ46−2ζ14−2ζ460000000000000000000000000000
χ6622-2-2−2i−2i2i2i-22-222-222−2i2i2i−2i2i−2i-2-2−2i−2i2i2i2-2-2-2222i−2i−2i2i2i−2i000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000000002ζ10+2ζ26−2ζ10−2ζ262ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46−2ζ14−2ζ462ζ14+2ζ460000000000000000000000000000
χ6722-2-2−2i−2i2i2i-22-2-12-22-1−2i2i2i−2i2i−2i11ii−i−i-1111-1-1−iii−i−ii00003−33−3−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ460000i3−i3i3−i3ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14+ζ46ζ14−ζ46−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ2600000000000000000000
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χ938-88i−8i8ζ14+8ζ46−8ζ14−8ζ46−8ζ10−8ζ268ζ10+8ζ26000-40004000000−4i4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ2600000000000000000000000000000000000000000000000000000000000000000000
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χ958-8−8i8i−8ζ10−8ζ268ζ10+8ζ268ζ14+8ζ46−8ζ14−8ζ46000-400040000004i−4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ4600000000000000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i8ζ10+8ζ26−8ζ10−8ζ26−8ζ14−8ζ468ζ14+8ζ46000-400040000004i−4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ4600000000000000000000000000000000000000000000000000000000000000000000

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