Finite Group Databasebeta

← Group #10695147

Character table — Group #10695147

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12224444223444444444466612121212668888888812121212121212121212242424242424242424242424242424248888888888888888444412121212121212128888
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
χ91111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ101111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ111111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ121111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ131111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ1722222222222-2-2-2-222-2-2-2-222222222222-2-222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222-2-2-2-222-2-2-2-2222222222-2-222-2-222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
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
χ232222222222-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ242222222222-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ252222222222-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-222-2-22211111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ262222222222-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-222-2-22211111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ2722222222-2-2222-2-2-2-222-2-22222222-2-20000000022-2-222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ2822222222-2-2222-2-2-2-222-2-22222222-2-20000000022-2-222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2922222222-2-22-2-222-2-2-2-2222222222-2-200000000-2-222-2-222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ3022222222-2-22-2-222-2-2-2-2222222222-2-200000000-2-222-2-222-2-20000000000000000-2-222-2-222000000000000000000000000
χ312222-2-2-2-222222-2-2-2-2-2-222222-2-2-2-2220000000022-2-2-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-222222-2-2-2-2-2-222222-2-2-2-2220000000022-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-222-2-222-2-2222-2-2-2-22200000000-2-22222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ342222-2-2-2-2222-2-222-2-222-2-2222-2-2-2-22200000000-2-22222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ352222-2-2-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-222-2-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ362222-2-2-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-2-2-2-2-1222222-2-2-2-2-1-1-11111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ382222-2-2-2-2-2-2-1222222-2-2-2-2-1-1-11111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ392222-2-2-2-2-2-2-1222222-2-2-2-2-1-1-1111111-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ402222-2-2-2-2-2-2-1222222-2-2-2-2-1-1-1111111-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ412222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-111111122-2-2-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ422222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-111111122-2-2-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ432222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-1111111-2-22222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-1111111-2-22222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ452-22-22i2i−2i−2i002002-200002i−2i-22-22i2i−2i−2i002−22−2−i2i2−i2i2002-2002i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ231−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ462-22-22i2i−2i−2i002002-200002i−2i-22-22i2i−2i−2i002−22−2−i2i2−i2i2002-2002i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ472-22-22i2i−2i−2i002002-200002i−2i-22-22i2i−2i−2i00−22−22i2−i2i2−i2002-2002i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ482-22-22i2i−2i−2i002002-200002i−2i-22-22i2i−2i−2i00−22−22i2−i2i2−i2002-2002i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ231−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ492-22-22i2i−2i−2i00200-220000−2i2i-22-22i2i−2i−2i002−2−22−i2i2i2−i200-2200−2i2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ502-22-22i2i−2i−2i00200-220000−2i2i-22-22i2i−2i−2i002−2−22−i2i2i2−i200-2200−2i2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i22ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ512-22-22i2i−2i−2i00200-220000−2i2i-22-22i2i−2i−2i00−222−2i2−i2−i2i200-2200−2i2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ522-22-22i2i−2i−2i00200-220000−2i2i-22-22i2i−2i−2i00−222−2i2−i2−i2i200-2200−2i2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i22ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ532-22-2−2i−2i2i2i002002-20000−2i2i-22-2−2i−2i2i2i002−22−2i2−i2i2−i2002-200−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ131+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ542-22-2−2i−2i2i2i002002-20000−2i2i-22-2−2i−2i2i2i002−22−2i2−i2i2−i2002-200−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ552-22-2−2i−2i2i2i002002-20000−2i2i-22-2−2i−2i2i2i00−22−22−i2i2−i2i2002-200−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ562-22-2−2i−2i2i2i002002-20000−2i2i-22-2−2i−2i2i2i00−22−22−i2i2−i2i2002-200−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ131+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ572-22-2−2i−2i2i2i00200-2200002i−2i-22-2−2i−2i2i2i002−2−22i2−i2−i2i200-22002i−2i0022−2−2−2−222i2i2−i2−i2−i2−i2i2i22ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ582-22-2−2i−2i2i2i00200-2200002i−2i-22-2−2i−2i2i2i002−2−22i2−i2−i2i200-22002i−2i0022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ592-22-2−2i−2i2i2i00200-2200002i−2i-22-2−2i−2i2i2i00−222−2−i2i2i2−i200-22002i−2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i22ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ602-22-2−2i−2i2i2i00200-2200002i−2i-22-2−2i−2i2i2i00−222−2−i2i2i2−i200-22002i−2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ6144444444-4-4-244-4-4-4-444-4-4-2-2-2-2-2-2-22200000000-2-222-2-22222000000000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-444-4-4-4-444-2-2-2-2-2-2-2220000000022-2-222-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-4-444-244-4-4-4-4-4-444-2-2-22222-2-200000000-2-22222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-4-444-2-4-444-4-444-4-4-2-2-22222-2-20000000022-2-2-2-22222000000000000000000000000000000000000000000000000
χ6544-4-44-44-44-4400004-400004-4-44-44-44-400000000000000004-4000000000000000000000000000000000000000000000000
χ6644-4-44-44-44-4-200004-40000-222-22-22-220000000000000000-22−2i32i3−2i32i30000−2i32i3−2i32i3000000000000000000000000000000000000
χ6744-4-44-44-44-4-200004-40000-222-22-22-220000000000000000-222i3−2i32i3−2i300002i3−2i32i3−2i3000000000000000000000000000000000000
χ6844-4-44-44-4-4440000-4400004-4-44-44-4-440000000000000000-44000000000000000000000000000000000000000000000000
χ6944-4-44-44-4-44-20000-440000-222-22-222-200000000000000002-20000−2i32i3−2i32i30000−2i32i3−2i32i300000000000000000000000000000000
χ7044-4-44-44-4-44-20000-440000-222-22-222-200000000000000002-200002i3−2i32i3−2i300002i3−2i32i3−2i300000000000000000000000000000000
χ7144-4-4-44-444-440000-4400004-4-4-44-444-40000000000000000-44000000000000000000000000000000000000000000000000
χ7244-4-4-44-444-4-20000-440000-2222-22-2-2200000000000000002-20000−2i32i3−2i32i300002i3−2i32i3−2i300000000000000000000000000000000
χ7344-4-4-44-444-4-20000-440000-2222-22-2-2200000000000000002-200002i3−2i32i3−2i30000−2i32i3−2i32i300000000000000000000000000000000
χ7444-4-4-44-44-44400004-400004-4-4-44-44-4400000000000000004-4000000000000000000000000000000000000000000000000
χ7544-4-4-44-44-44-200004-40000-2222-22-22-20000000000000000-22−2i32i3−2i32i300002i3−2i32i3−2i3000000000000000000000000000000000000
χ7644-4-4-44-44-44-200004-40000-2222-22-22-20000000000000000-222i3−2i32i3−2i30000−2i32i3−2i32i3000000000000000000000000000000000000
χ774-44-44i4i−4i−4i00-2004-400004i−4i2-22−2i−2i2i2i0022−2222−22−2i22i2−2i22i200-2200−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ784-44-44i4i−4i−4i00-2004-400004i−4i2-22−2i−2i2i2i00−2222−22222i2−2i22i2−2i200-2200−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ794-44-44i4i−4i−4i00-200-440000−4i4i2-22−2i−2i2i2i0022−22−2222−2i22i22i2−2i2002-2002i−2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ804-44-44i4i−4i−4i00-200-440000−4i4i2-22−2i−2i2i2i00−222222−222i2−2i2−2i22i2002-2002i−2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ814-44-4−4i−4i4i4i00-2004-40000−4i4i2-222i2i−2i−2i0022−2222−222i2−2i22i2−2i200-22002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ824-44-4−4i−4i4i4i00-2004-40000−4i4i2-222i2i−2i−2i00−2222−2222−2i22i2−2i22i200-22002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ834-44-4−4i−4i4i4i00-200-4400004i−4i2-222i2i−2i−2i0022−22−22222i2−2i2−2i22i2002-200−2i2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ844-44-4−4i−4i4i4i00-200-4400004i−4i2-222i2i−2i−2i00−222222−22−2i22i22i2−2i2002-200−2i2i0022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ854-4-444i−4i−4i4i0044-400004i−4i00-4-444i−4i−4i4i00000000004-4004i−4i0000000000000000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i004-440000−4i4i00-4-444i−4i−4i4i0000000000-4400−4i4i0000000000000000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i00-24-400004i−4i0022-2−2i2i2i−2i0000000000-2200−2i2i0000i6−i6−i6i6i6−i6−i6i66−6−666−6−6600000000000000000000000000000000
χ884-4-444i−4i−4i4i00-24-400004i−4i0022-2−2i2i2i−2i0000000000-2200−2i2i0000−i6i6i6−i6−i6i6i6−i6−666−6−666−600000000000000000000000000000000
χ894-4-444i−4i−4i4i00-2-440000−4i4i0022-2−2i2i2i−2i00000000002-2002i−2i0000i6−i6−i6i6−i6i6i6−i66−6−66−666−600000000000000000000000000000000
χ904-4-444i−4i−4i4i00-2-440000−4i4i0022-2−2i2i2i−2i00000000002-2002i−2i0000−i6i6i6−i6i6−i6−i6i6−666−66−6−6600000000000000000000000000000000
χ914-4-44−4i4i4i−4i0044-40000−4i4i00-4-44−4i4i4i−4i00000000004-400−4i4i0000000000000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i004-4400004i−4i00-4-44−4i4i4i−4i0000000000-44004i−4i0000000000000000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i00-24-40000−4i4i0022-22i−2i−2i2i0000000000-22002i−2i0000i6−i6−i6i6i6−i6−i6i6−666−6−666−600000000000000000000000000000000
χ944-4-44−4i4i4i−4i00-24-40000−4i4i0022-22i−2i−2i2i0000000000-22002i−2i0000−i6i6i6−i6−i6i6i6−i66−6−666−6−6600000000000000000000000000000000
χ954-4-44−4i4i4i−4i00-2-4400004i−4i0022-22i−2i−2i2i00000000002-200−2i2i0000i6−i6−i6i6−i6i6i6−i6−666−66−6−6600000000000000000000000000000000
χ964-4-44−4i4i4i−4i00-2-4400004i−4i0022-22i−2i−2i2i00000000002-200−2i2i0000−i6i6i6−i6i6−i6−i6i66−6−66−666−600000000000000000000000000000000

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