Finite Group Databasebeta

← Group #10695068

Character table — Group #10695068

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111111122222222222222222222222222222222222244444444444444444444444444446666666666666666666666666666666616161616161616161616161648484848
order12224444223444444444466688888888888888881212121266121212121212121212122424242424242424242424242424242444444444444444448888888888888888888824242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−iii−i−i1-11-1
χ101111-1-1-1-1-1-111111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii−i−iii-11-11
χ111111-1-1-1-1-1-111111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−iii−i−i-11-11
χ121111-1-1-1-1-1-111111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii−i−iii1-11-1
χ131111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiii−i−iiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−iii−i−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ172222222222222-2-2-2-2-2-2-2-2222000000000000000022222222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2222000000000000000022222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ192222222222-12222222222-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000002222-1-1-1-1-1-1-1-10000
χ202222222222-12222222222-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000-2-2-2-2111111110000
χ212222222222-12222222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000000000000000000022-2-2-1-1-1-111110000
χ222222222222-12222222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000000000-2-2221111-1-1-1-10000
χ2322222222-2-22-2-222-2-2-2-22222200000000000000002222-2-2-2-22222-2-2-2-2000000000000000000000000000000002222-2-2-2-22222-2-2-2-20000000000000000
χ2422222222-2-22-2-222-2-2-2-22222200000000000000002222-2-2-2-22222-2-2-2-200000000000000000000000000000000-2-2-2-22222-2-2-2-222220000000000000000
χ2522222222-2-22-2-2-2-22222-2-22222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ2622222222-2-22-2-2-2-22222-2-2222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ2722222222-2-2-1-2-2-2-22222-2-2-1-1-12222-2-2-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-2-2-1-2-2-2-22222-2-2-1-1-12222-2-2-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-2-2-1-2-2-2-22222-2-2-1-1-1-2-2-2-22222-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-2-2-1-2-2-2-22222-2-2-1-1-1-2-2-2-22222-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-2-2-2222-2-22222-2-2-2-22220000000000000000-2-2-2-222-2-222-2-222-2-2000000000000000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000
χ322222-2-2-2-2222-2-22222-2-2-2-22220000000000000000-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-2-2-22222-1-1-12222-2-2-2-2-2-2-2-222221111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-10000000000000000000000000000000000003−3−333−3−330000
χ362222-2-2-2-222-1-2-2-2-2-2-22222-1-1-12222-2-2-2-2-2-2-2-222221111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1000000000000000000000000000000000000−333−3−333−30000
χ372222-2-2-2-222-1-2-2-2-2-2-22222-1-1-1-2-2-2-222222222-2-2-2-21111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111110000000000000000000000000000000000003−3−33−333−30000
χ382222-2-2-2-222-1-2-2-2-2-2-22222-1-1-1-2-2-2-222222222-2-2-2-21111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111000000000000000000000000000000000000−333−33−3−330000
χ392222-2-2-2-2-2-2222-2-222-2-2222220000000000000000-2-2-2-2-2-222-2-22222-2-200000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ402222-2-2-2-2-2-2222-2-222-2-2222220000000000000000-2-2-2-2-2-222-2-22222-2-20000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ412222-2-2-2-2-2-2-12222-2-222-2-2-1-1-122222222-2-2-2-2-2-2-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000000000000000000000002i−2i2i−2i−i−iii−i−iii0000
χ422222-2-2-2-2-2-2-12222-2-222-2-2-1-1-122222222-2-2-2-2-2-2-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000000000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ432222-2-2-2-2-2-2-12222-2-222-2-2-1-1-1-2-2-2-2-2-2-2-222222222111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1000000000000000000000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ442222-2-2-2-2-2-2-12222-2-222-2-2-1-1-1-2-2-2-2-2-2-2-222222222111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ4522-2-222-2-22-222-2000000002-2-222−2−222−2−222−2−222−2−222-2-22-22-20000000022−2−222−2−222−2−222−2−2000022-2-2000022-2-222−2−222−2−222−2−222−2−20000000000000000
χ4622-2-222-2-22-222-2000000002-2-222−2−222−2−222−2−222−2−222-2-22-22-20000000022−2−222−2−222−2−222−2−20000-2-2220000-2-222−2−222−2−222−2−222−2−2220000000000000000
χ4722-2-222-2-22-222-2000000002-2-2−2−222−2−222−2−222−2−22222-2-22-22-200000000−2−222−2−222−2−222−2−222000022-2-2000022-2-2−2−222−2−222−2−222−2−2220000000000000000
χ4822-2-222-2-22-222-2000000002-2-2−2−222−2−222−2−222−2−22222-2-22-22-200000000−2−222−2−222−2−222−2−2220000-2-2220000-2-22222−2−222−2−222−2−222−2−20000000000000000
χ4922-2-222-2-2-222-22000000002-2-222−2−2−2−22222−2−2−2−22222-2-2-22-220000000022−2−2−2−22222−2−2−2−22222-2-2000022-2-2000022−2−2−2−22222−2−2−2−2220000000000000000
χ5022-2-222-2-2-222-22000000002-2-222−2−2−2−22222−2−2−2−22222-2-2-22-220000000022−2−2−2−22222−2−2−2−222-2-2220000-2-2220000−2−22222−2−2−2−22222−2−20000000000000000
χ5122-2-222-2-2-222-22000000002-2-2−2−22222−2−2−2−22222−2−222-2-2-22-2200000000−2−22222−2−2−2−22222−2−222-2-2000022-2-20000−2−22222−2−2−2−22222−2−20000000000000000
χ5222-2-222-2-2-222-22000000002-2-2−2−22222−2−2−2−22222−2−222-2-2-22-2200000000−2−22222−2−2−2−22222−2−2-2-2220000-2-222000022−2−2−2−22222−2−2−2−2220000000000000000
χ5322-2-2-2-2222-22-22000000002-2-222−2−2−2−222−2−22222−2−2-2-2222-2-220000000022−2−2−2−222−2−22222−2−22i2i−2i−2i0000−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5422-2-2-2-2222-22-22000000002-2-222−2−2−2−222−2−22222−2−2-2-2222-2-220000000022−2−2−2−222−2−22222−2−2−2i−2i2i2i00002i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5522-2-2-2-2222-22-22000000002-2-2−2−22222−2−222−2−2−2−222-2-2222-2-2200000000−2−22222−2−222−2−2−2−2222i2i−2i−2i0000−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5622-2-2-2-2222-22-22000000002-2-2−2−22222−2−222−2−2−2−222-2-2222-2-2200000000−2−22222−2−222−2−2−2−222−2i−2i2i2i00002i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5722-2-2-2-222-2222-2000000002-2-222−2−222−2−2−2−222−2−222-2-222-222-20000000022−2−222−2−2−2−222−2−22200002i2i−2i−2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ5822-2-2-2-222-2222-2000000002-2-222−2−222−2−2−2−222−2−222-2-222-222-20000000022−2−222−2−2−2−222−2−2220000−2i−2i2i2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ5922-2-2-2-222-2222-2000000002-2-2−2−222−2−22222−2−222−2−2-2-222-222-200000000−2−222−2−22222−2−222−2−200002i2i−2i−2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ6022-2-2-2-222-2222-2000000002-2-2−2−222−2−22222−2−222−2−2-2-222-222-200000000−2−222−2−22222−2−222−2−20000−2i−2i2i2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ612-22-22i−2i2i−2i00200002i−2i2-200-22-200002i−2i2i−2i00002-22-22i−2i2i−2i000000002i−2i2-200002i−2i2i−2i00002-22-21+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ622-22-22i−2i2i−2i00200002i−2i2-200-22-200002i−2i2i−2i00002-22-22i−2i2i−2i000000002i−2i2-200002i−2i2i−2i00002-22-2−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ632-22-22i−2i2i−2i00200002i−2i2-200-22-20000−2i2i−2i2i0000-22-222i−2i2i−2i000000002i−2i2-20000−2i2i−2i2i0000-22-221+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ642-22-22i−2i2i−2i00200002i−2i2-200-22-20000−2i2i−2i2i0000-22-222i−2i2i−2i000000002i−2i2-20000−2i2i−2i2i0000-22-22−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ652-22-22i−2i2i−2i0020000−2i2i-2200-22-22i−2i2i−2i00002-22-200002i−2i2i−2i00000000−2i2i-222i−2i2i−2i00002-22-200001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000000000
χ662-22-22i−2i2i−2i0020000−2i2i-2200-22-22i−2i2i−2i00002-22-200002i−2i2i−2i00000000−2i2i-222i−2i2i−2i00002-22-20000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.