Finite Group Databasebeta

← Group #10695112

Character table — Group #10695112

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12224444223444444444466612121212668888888812121212121212121212242424242424242424242424242424244444444488888888888824242424242424244444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i1-11-1
χ101111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-11-11
χ111111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-11-11
χ121111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii1-11-1
χ131111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ172222222222222-2-2-2-2-2-2-2-22222222220000000022-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222220000000022-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-12222222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ202222222222-12222222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ222222222222-12222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ2322222222-2-22-2-222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ2422222222-2-22-2-222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2522222222-2-22-2-2-2-22222-2-22222222-2-222-2-222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2622222222-2-22-2-2-2-22222-2-22222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2722222222-2-2-1-2-2-2-22222-2-2-1-1-1-1-1-1-11122-2-222-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-2-2-1-2-2-2-22222-2-2-1-1-1-1-1-1-11122-2-222-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-2-2-1-2-2-2-22222-2-2-1-1-1-1-1-1-111-2-222-2-222111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-2-2-1-2-2-2-22222-2-2-1-1-1-1-1-1-111-2-222-2-222111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22200000000-2-222-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22200000000-2-222-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-222-2-22222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-122-2-2-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-1000000000000000000003−3−333−3−330000
χ362222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-122-2-2-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000−333−3−333−30000
χ372222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-1-2-22222-2-21111-1-111-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ382222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-1-2-22222-2-21111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ392222-2-2-2-2-2-2222-2-222-2-222222-2-2-2-2-2-20000000022-2-22222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-2-2-2222-2-222-2-222222-2-2-2-2-2-20000000022-2-22222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412222-2-2-2-2-2-2-12222-2-222-2-2-1-1-11111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ422222-2-2-2-2-2-2-12222-2-222-2-2-1-1-11111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ432222-2-2-2-2-2-2-12222-2-222-2-2-1-1-1111111-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ442222-2-2-2-2-2-2-12222-2-222-2-2-1-1-1111111-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ452-22-22i2i−2i−2i002002-200002i−2i2-2-22i2i−2i−2i002−22−2−i2i2−i2i2002-22i−2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ462-22-22i2i−2i−2i002002-200002i−2i2-2-22i2i−2i−2i002−22−2−i2i2−i2i2002-22i−2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ472-22-22i2i−2i−2i002002-200002i−2i2-2-22i2i−2i−2i00−22−22i2−i2i2−i2002-22i−2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ482-22-22i2i−2i−2i002002-200002i−2i2-2-22i2i−2i−2i00−22−22i2−i2i2−i2002-22i−2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ492-22-22i2i−2i−2i00200-220000−2i2i2-2-22i2i−2i−2i002−2−22−i2i2i2−i200-22−2i2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i21+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ502-22-22i2i−2i−2i00200-220000−2i2i2-2-22i2i−2i−2i002−2−22−i2i2i2−i200-22−2i2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ512-22-22i2i−2i−2i00200-220000−2i2i2-2-22i2i−2i−2i00−222−2i2−i2−i2i200-22−2i2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ522-22-22i2i−2i−2i00200-220000−2i2i2-2-22i2i−2i−2i00−222−2i2−i2−i2i200-22−2i2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ532-22-2−2i−2i2i2i002002-20000−2i2i2-2-2−2i−2i2i2i002−22−2i2−i2i2−i2002-2−2i2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ542-22-2−2i−2i2i2i002002-20000−2i2i2-2-2−2i−2i2i2i002−22−2i2−i2i2−i2002-2−2i2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ552-22-2−2i−2i2i2i002002-20000−2i2i2-2-2−2i−2i2i2i00−22−22−i2i2−i2i2002-2−2i2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ562-22-2−2i−2i2i2i002002-20000−2i2i2-2-2−2i−2i2i2i00−22−22−i2i2−i2i2002-2−2i2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ572-22-2−2i−2i2i2i00200-2200002i−2i2-2-2−2i−2i2i2i002−2−22i2−i2−i2i200-222i−2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ582-22-2−2i−2i2i2i00200-2200002i−2i2-2-2−2i−2i2i2i002−2−22i2−i2−i2i200-222i−2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ592-22-2−2i−2i2i2i00200-2200002i−2i2-2-2−2i−2i2i2i00−222−2−i2i2i2−i200-222i−2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ602-22-2−2i−2i2i2i00200-2200002i−2i2-2-2−2i−2i2i2i00−222−2−i2i2i2−i200-222i−2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ614444444444-244-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-200000000-2-222222222000000000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-444-4-4-4-444-2-2-2-2-2-2-2220000000022-2-2-2-22222000000000000000000000000000000000000000000000000
χ634444-4-4-4-444-2-4-44444-4-4-4-4-2-2-22222-2-20000000022-2-222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-4-244-4-444-4-444-2-2-222222200000000-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ6544-4-44-44-44-444-400000000-44-44-44-44-4000000004-400000000000000000000000000000000000000000000000000000000
χ6644-4-44-44-44-4-24-4000000002-22-22-22-2200000000-22000000006−66−66−66−66−66−66−66−600000000000000000000000000000000
χ6744-4-44-44-44-4-24-4000000002-22-22-22-2200000000-2200000000−66−66−66−66−66−66−66−6600000000000000000000000000000000
χ6844-4-44-44-4-444-4400000000-44-44-44-4-4400000000-4400000000000000000000000000000000000000000000000000000000
χ6944-4-44-44-4-44-2-44000000002-22-22-222-2000000002-2000000006−66−6−66−666−66−6−66−6600000000000000000000000000000000
χ7044-4-44-44-4-44-2-44000000002-22-22-222-2000000002-200000000−66−666−66−6−66−666−66−600000000000000000000000000000000
χ7144-4-4-44-444-44-4400000000-44-4-44-444-400000000-4400000000000000000000000000000000000000000000000000000000
χ7244-4-4-44-444-4-2-44000000002-222-22-2-22000000002-2000000006−66−6−66−66−66−666−66−600000000000000000000000000000000
χ7344-4-4-44-444-4-2-44000000002-222-22-2-22000000002-200000000−66−666−66−66−66−6−66−6600000000000000000000000000000000
χ7444-4-4-44-44-4444-400000000-44-4-44-44-44000000004-400000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-44-44-24-4000000002-222-22-22-200000000-22000000006−66−66−66−6−66−66−66−6600000000000000000000000000000000
χ7644-4-4-44-44-44-24-4000000002-222-22-22-200000000-2200000000−66−66−66−666−66−66−66−600000000000000000000000000000000
χ774-44-44i4i−4i−4i00-2004-400004i−4i-222−2i−2i2i2i0022−2222−22−2i22i2−2i22i200-22−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ784-44-44i4i−4i−4i00-2004-400004i−4i-222−2i−2i2i2i00−2222−22222i2−2i22i2−2i200-22−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ794-44-44i4i−4i−4i00-200-440000−4i4i-222−2i−2i2i2i0022−22−2222−2i22i22i2−2i2002-22i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ804-44-44i4i−4i−4i00-200-440000−4i4i-222−2i−2i2i2i00−222222−222i2−2i2−2i22i2002-22i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ814-44-4−4i−4i4i4i00-2004-40000−4i4i-2222i2i−2i−2i0022−2222−222i2−2i22i2−2i200-222i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ824-44-4−4i−4i4i4i00-2004-40000−4i4i-2222i2i−2i−2i00−2222−2222−2i22i2−2i22i200-222i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ834-44-4−4i−4i4i4i00-200-4400004i−4i-2222i2i−2i−2i0022−22−22222i2−2i2−2i22i2002-2−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ844-44-4−4i−4i4i4i00-200-4400004i−4i-2222i2i−2i−2i00−222222−22−2i22i22i2−2i2002-2−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ854-4-444i−4i−4i4i00400004i−4i4-400-4-444i−4i−4i4i00000000000000004i−4i4-4000000000000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i0040000−4i4i-4400-4-444i−4i−4i4i0000000000000000−4i4i-44000000000000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i00-200004i−4i4-40022-2−2i2i2i−2i0000000000000000−2i2i-22000023−23−23230000−2i32i32i3−2i300000000000000000000000000000000
χ884-4-444i−4i−4i4i00-200004i−4i4-40022-2−2i2i2i−2i0000000000000000−2i2i-220000−232323−2300002i3−2i3−2i32i300000000000000000000000000000000
χ894-4-444i−4i−4i4i00-20000−4i4i-440022-2−2i2i2i−2i00000000000000002i−2i2-223−23−23230000−2i32i32i3−2i3000000000000000000000000000000000000
χ904-4-444i−4i−4i4i00-20000−4i4i-440022-2−2i2i2i−2i00000000000000002i−2i2-2−232323−2300002i3−2i3−2i32i3000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i00400004i−4i-4400-4-44−4i4i4i−4i00000000000000004i−4i-44000000000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i0040000−4i4i4-400-4-44−4i4i4i−4i0000000000000000−4i4i4-4000000000000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i00-200004i−4i-440022-22i−2i−2i2i0000000000000000−2i2i2-223−23−232300002i3−2i3−2i32i3000000000000000000000000000000000000
χ944-4-44−4i4i4i−4i00-200004i−4i-440022-22i−2i−2i2i0000000000000000−2i2i2-2−232323−230000−2i32i32i3−2i3000000000000000000000000000000000000
χ954-4-44−4i4i4i−4i00-20000−4i4i4-40022-22i−2i−2i2i00000000000000002i−2i-22000023−23−232300002i3−2i3−2i32i300000000000000000000000000000000
χ964-4-44−4i4i4i−4i00-20000−4i4i4-40022-22i−2i−2i2i00000000000000002i−2i-220000−232323−230000−2i32i32i3−2i300000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.