Finite Group Databasebeta

← Group #10705296

Character table — Group #10705296

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12224444344446668888888812121212121212121616161616161616242424242424242448484848484848484848484848484848244488881616161616161616448812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ121111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ131111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ141111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ151111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ161111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ172222222222222222-2-2-2-2-2-2-2-22222222200000000-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222222200000000-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ19222222222-2-2-2-2222000000002222-2-2-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−222-2-2000022−2−222−2−20000000000000000
χ20222222222-2-2-2-2222000000002222-2-2-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−2-2-2220000−2−222−2−2220000000000000000
χ21222222222-2-2-2-2222000000002222-2-2-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−2222222-2-20000−2−222−2−2220000000000000000
χ22222222222-2-2-2-2222000000002222-2-2-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−22222-2-222000022−2−222−2−20000000000000000
χ2322222222-12222-1-1-122222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2422222222-12222-1-1-122222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2522222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ2622222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ272222-2-2-2-2222-2-222200000000-2-2-2-222-2-2−i2−i2i2i2i2i2−i2−i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-2-220000−i2−i2i2i2i2i2−i2−i20000000000000000
χ282222-2-2-2-2222-2-222200000000-2-2-2-222-2-2−i2−i2i2i2i2i2−i2−i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-222-20000i2i2−i2−i2−i2−i2i2i20000000000000000
χ292222-2-2-2-2222-2-222200000000-2-2-2-222-2-2i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-2-220000i2i2−i2−i2−i2−i2i2i20000000000000000
χ302222-2-2-2-2222-2-222200000000-2-2-2-222-2-2i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-222-20000−i2−i2i2i2i2i2−i2−i20000000000000000
χ312222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-2-2-22200000000-2-2-2-2222200000000000000002-22-2-2-222000000000000000000000000
χ322222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-2-2-22200000000-2-2-2-222220000000000000000-22-2222-2-2000000000000000000000000
χ332222-2-2-2-2-1-2-222-1-1-12222-2-2-2-2111111-1-12i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-22i−2i-1-111−i−iii0000
χ342222-2-2-2-2-1-2-222-1-1-12222-2-2-2-2111111-1-12i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ352222-2-2-2-2-1-2-222-1-1-12222-2-2-2-2111111-1-1−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ362222-2-2-2-2-1-2-222-1-1-12222-2-2-2-2111111-1-1−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ372-22-22i−2i2i−2i22i−2i2-2-22-2000000002i−2i2i−2i2i−2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00002i−2i2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ382-22-22i−2i2i−2i22i−2i2-2-22-2000000002i−2i2i−2i2i−2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000−2i2i-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ392-22-22i−2i2i−2i22i−2i2-2-22-2000000002i−2i2i−2i2i−2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00002i−2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ402-22-22i−2i2i−2i22i−2i2-2-22-2000000002i−2i2i−2i2i−2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000−2i2i-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ412-22-22i−2i2i−2i2−2i2i-22-22-222-2-22i2i−2i−2i2i−2i2i−2i−2i2i-220000000022-2-22i2i−2i−2i000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ262ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ460000000000000000
χ422-22-22i−2i2i−2i2−2i2i-22-22-222-2-22i2i−2i−2i2i−2i2i−2i−2i2i-220000000022-2-22i2i−2i−2i0000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ26−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ460000000000000000
χ432-22-22i−2i2i−2i2−2i2i-22-22-2-2-222−2i−2i2i2i2i−2i2i−2i−2i2i-222ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ46−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ26-2-222−2i−2i2i2i2ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ2600000000000000000000000000000000
χ442-22-22i−2i2i−2i2−2i2i-22-22-2-2-222−2i−2i2i2i2i−2i2i−2i−2i2i-22−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ462ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ26-2-222−2i−2i2i2i−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ2600000000000000000000000000000000
χ452-22-22i−2i2i−2i-1−2i2i-221-11-2-222−2i−2i2i2i−ii−iii−i1-12ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ46−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ2611-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2600000000000000000000−i3i33−3−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ260000
χ462-22-22i−2i2i−2i-1−2i2i-221-11-2-222−2i−2i2i2i−ii−iii−i1-12ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ46−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ2611-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2600000000000000000000i3−i3−33ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ260000
χ472-22-22i−2i2i−2i-1−2i2i-221-11-2-222−2i−2i2i2i−ii−iii−i1-1−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ462ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ2611-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2600000000000000000000−i3i33−3ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ260000
χ482-22-22i−2i2i−2i-1−2i2i-221-11-2-222−2i−2i2i2i−ii−iii−i1-1−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ462ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ2611-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2600000000000000000000i3−i3−33−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ260000
χ492-22-2−2i2i−2i2i22i−2i-22-22-222-2-2−2i−2i2i2i−2i2i−2i2i2i−2i-220000000022-2-2−2i−2i2i2i0000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ46−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ260000000000000000
χ502-22-2−2i2i−2i2i22i−2i-22-22-222-2-2−2i−2i2i2i−2i2i−2i2i2i−2i-220000000022-2-2−2i−2i2i2i000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ462ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ260000000000000000
χ512-22-2−2i2i−2i2i22i−2i-22-22-2-2-2222i2i−2i−2i−2i2i−2i2i2i−2i-22−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ262ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ46-2-2222i2i−2i−2i−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ4600000000000000000000000000000000
χ522-22-2−2i2i−2i2i22i−2i-22-22-2-2-2222i2i−2i−2i−2i2i−2i2i2i−2i-222ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ26−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ46-2-2222i2i−2i−2i2ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ26−2ζ10−2ζ26−2ζ10−2ζ26−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ462ζ14+2ζ462ζ14+2ζ462ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ4600000000000000000000000000000000
χ532-22-2−2i2i−2i2i2−2i2i2-2-22-200000000−2i2i−2i2i−2i2i2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00002i−2i-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ542-22-2−2i2i−2i2i2−2i2i2-2-22-200000000−2i2i−2i2i−2i2i2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000−2i2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ552-22-2−2i2i−2i2i2−2i2i2-2-22-200000000−2i2i−2i2i−2i2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00002i−2i-221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ562-22-2−2i2i−2i2i2−2i2i2-2-22-200000000−2i2i−2i2i−2i2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000−2i2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ572-22-2−2i2i−2i2i-12i−2i-221-11-2-2222i2i−2i−2ii−ii−i−ii1-1−2ζ10−2ζ262ζ10+2ζ262ζ10+2ζ26−2ζ10−2ζ262ζ14+2ζ46−2ζ14−2ζ46−2ζ14−2ζ462ζ14+2ζ4611-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4600000000000000000000−i3i3−33−ζ10+ζ26ζ10−ζ26ζ14−ζ46−ζ14+ζ460000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.