Finite Group Databasebeta

← Group #10695132

Character table — Group #10695132

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111111122222222222222222222222222222222222244444444444444444444444444446666666666666666666666666666666616161616161616161616161648484848
order12224444223444444444466688888888888888881212121266121212121212121212122424242424242424242424242424242488888888888888888888888888888888888824242424242424242444
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
χ91111-1-1-1-1-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−iii−i−i1-11-1
χ101111-1-1-1-1-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii−i−iii-11-11
χ111111-1-1-1-1-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−iii−i−i-11-11
χ121111-1-1-1-1-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii−i−iii1-11-1
χ131111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiii−i−iiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−iii−i−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ1722222222222-2-2-2-222-2-2-2-22222222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222-2-2-2-222-2-2-2-2222-2-2-2-22222-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
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
χ232222222222-1-2-2-2-222-2-2-2-2-1-1-12222-2-2-2-22222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ242222222222-1-2-2-2-222-2-2-2-2-1-1-12222-2-2-2-22222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ252222222222-1-2-2-2-222-2-2-2-2-1-1-1-2-2-2-22222-2-2-2-22222-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ262222222222-1-2-2-2-222-2-2-2-2-1-1-1-2-2-2-22222-2-2-2-22222-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ2722222222-2-2222-2-2-2-222-2-222200000000000000002222-2-222-2-222-2-2-2-2000000000000000000000000000000002222-2-2-2-22222-2-2-2-20000000000000000
χ2822222222-2-2222-2-2-2-222-2-222200000000000000002222-2-222-2-222-2-2-2-200000000000000000000000000000000-2-2-2-22222-2-2-2-222220000000000000000
χ2922222222-2-22-2-222-2-2-2-22222200000000000000002222-2-2-2-222-2-222-2-200000000000000002222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ3022222222-2-22-2-222-2-2-2-22222200000000000000002222-2-2-2-222-2-222-2-20000000000000000-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ312222-2-2-2-222222-2-2-2-2-2-2222220000000000000000-2-2-2-22222-2-2-2-222-2-2000000000000000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000
χ322222-2-2-2-222222-2-2-2-2-2-2222220000000000000000-2-2-2-22222-2-2-2-222-2-200000000000000000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-222-2-222-2-22220000000000000000-2-2-2-222-2-22222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ342222-2-2-2-2222-2-222-2-222-2-22220000000000000000-2-2-2-222-2-22222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ352222-2-2-2-2-2-22-2-2-2-22222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ362222-2-2-2-2-2-22-2-2-2-2222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-1222222-2-2-2-2-1-1-122222222-2-2-2-2-2-2-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000000000000000000000002i−2i2i−2i−i−iii−i−iii0000
χ382222-2-2-2-2-2-2-1222222-2-2-2-2-1-1-122222222-2-2-2-2-2-2-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000000000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ392222-2-2-2-2-2-2-1222222-2-2-2-2-1-1-1-2-2-2-2-2-2-2-222222222111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1000000000000000000000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ402222-2-2-2-2-2-2-1222222-2-2-2-2-1-1-1-2-2-2-2-2-2-2-222222222111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ412222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-12222-2-2-2-2-2-2-2-222221111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000000000000000000000003−3−333−3−330000
χ422222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-12222-2-2-2-2-2-2-2-222221111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000000000000000000000000000−333−3−333−30000
χ432222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-1-2-2-2-222222222-2-2-2-21111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000000000000000000000003−3−33−333−30000
χ442222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-1-2-2-2-222222222-2-2-2-21111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000000000000000000000−333−33−3−330000
χ4522-2-222-2-22-2200002-200002-2-200002i2i−2i−2i00002i2i−2i−2i22-2-22-2000000002-200002i2i−2i−2i00002i2i−2i−2i22−2−222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4622-2-222-2-22-2200002-200002-2-200002i2i−2i−2i00002i2i−2i−2i22-2-22-2000000002-200002i2i−2i−2i00002i2i−2i−2i−2−222−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4722-2-222-2-22-2200002-200002-2-20000−2i−2i2i2i0000−2i−2i2i2i22-2-22-2000000002-20000−2i−2i2i2i0000−2i−2i2i2i22−2−222−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4822-2-222-2-22-2200002-200002-2-20000−2i−2i2i2i0000−2i−2i2i2i22-2-22-2000000002-20000−2i−2i2i2i0000−2i−2i2i2i−2−222−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4922-2-222-2-2-2220000-2200002-2-22i2i−2i−2i00002i2i−2i−2i000022-2-2-2200000000-222i2i−2i−2i00002i2i−2i−2i000022−2−2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5022-2-222-2-2-2220000-2200002-2-22i2i−2i−2i00002i2i−2i−2i000022-2-2-2200000000-222i2i−2i−2i00002i2i−2i−2i0000−2−22222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5122-2-222-2-2-2220000-2200002-2-2−2i−2i2i2i0000−2i−2i2i2i000022-2-2-2200000000-22−2i−2i2i2i0000−2i−2i2i2i000022−2−2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5222-2-222-2-2-2220000-2200002-2-2−2i−2i2i2i0000−2i−2i2i2i000022-2-2-2200000000-22−2i−2i2i2i0000−2i−2i2i2i0000−2−22222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5322-2-2-2-2222-220000-2200002-2-22i2i−2i−2i0000−2i−2i2i2i0000-2-2222-200000000-222i2i−2i−2i0000−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−2−22222−2−222−2−2−2−2220000000000000000
χ5422-2-2-2-2222-220000-2200002-2-22i2i−2i−2i0000−2i−2i2i2i0000-2-2222-200000000-222i2i−2i−2i0000−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2−22222−2−20000000000000000
χ5522-2-2-2-2222-220000-2200002-2-2−2i−2i2i2i00002i2i−2i−2i0000-2-2222-200000000-22−2i−2i2i2i00002i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i222−2−2−2−222−2−22222−2−20000000000000000
χ5622-2-2-2-2222-220000-2200002-2-2−2i−2i2i2i00002i2i−2i−2i0000-2-2222-200000000-22−2i−2i2i2i00002i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−2−22222−2−222−2−2−2−2220000000000000000
χ5722-2-2-2-222-22200002-200002-2-200002i2i−2i−2i0000−2i−2i2i2i-2-222-22000000002-200002i2i−2i−2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2−222−2−22222−2−222−2−20000000000000000
χ5822-2-2-2-222-22200002-200002-2-200002i2i−2i−2i0000−2i−2i2i2i-2-222-22000000002-200002i2i−2i−2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i222−2−222−2−2−2−222−2−2220000000000000000
χ5922-2-2-2-222-22200002-200002-2-20000−2i−2i2i2i00002i2i−2i−2i-2-222-22000000002-20000−2i−2i2i2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i222−2−222−2−2−2−222−2−2220000000000000000
χ6022-2-2-2-222-22200002-200002-2-20000−2i−2i2i2i00002i2i−2i−2i-2-222-22000000002-20000−2i−2i2i2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2−222−2−22222−2−222−2−20000000000000000
χ612-22-22i−2i2i−2i002002-200002i−2i-22-22−22−22−22−2−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00002-2002i−2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ231−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−2i002002-200002i−2i-22-22−22−22−22−2−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00002-2002i−2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i200002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−1+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−2i002002-200002i−2i-22-2−22−22−22−22i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00002-2002i−2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i20000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
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χ1134-4-444i−4i−4i4i00-24-400004i−4i0022-2−2i22i22i2−2i2−2i22i22i2−2i2−222222−22−222222−22−2i2i2i−2i00-2200−2i2i0000i2−i2−i2i2i2−i2−i2i22−2−222−2−22000000000000000000000000000000000000000000000000
χ1144-4-444i−4i−4i4i00-24-400004i−4i0022-22i2−2i2−2i22i22i2−2i2−2i22i222−22−222222−22−2222−2i2i2i−2i00-2200−2i2i0000−i2i2i2−i2−i2i2i2−i2−222−2−222−2000000000000000000000000000000000000000000000000
χ1154-4-444i−4i−4i4i00-2-440000−4i4i0022-2−2i22i22i2−2i22i2−2i2−2i22i2−222222−2222−22−2222−2i2i2i−2i002-2002i−2i0000i2−i2−i2i2−i2i2i2−i22−2−22−222−2000000000000000000000000000000000000000000000000
χ1164-4-444i−4i−4i4i00-2-440000−4i4i0022-22i2−2i2−2i22i2−2i22i22i2−2i222−22−2222−222222−22−2i2i2i−2i002-2002i−2i0000−i2i2i2−i2i2−i2−i2i2−222−22−2−22000000000000000000000000000000000000000000000000
χ1174-4-44−4i4i4i−4i00-24-40000−4i4i0022-2−2i22i22i2−2i2−2i22i22i2−2i222−22−222222−22−22222i−2i−2i2i00-22002i−2i0000i2−i2−i2i2i2−i2−i2i2−222−2−222−2000000000000000000000000000000000000000000000000
χ1184-4-44−4i4i4i−4i00-24-40000−4i4i0022-22i2−2i2−2i22i22i2−2i2−2i22i2−222222−22−222222−222i−2i−2i2i00-22002i−2i0000−i2i2i2−i2−i2i2i2−i22−2−222−2−22000000000000000000000000000000000000000000000000
χ1194-4-44−4i4i4i−4i00-2-4400004i−4i0022-2−2i22i22i2−2i22i2−2i2−2i22i222−22−2222−222222−222i−2i−2i2i002-200−2i2i0000i2−i2−i2i2−i2i2i2−i2−222−22−2−22000000000000000000000000000000000000000000000000
χ1204-4-44−4i4i4i−4i00-2-4400004i−4i0022-22i2−2i2−2i22i2−2i22i22i2−2i2−222222−2222−22−22222i−2i−2i2i002-200−2i2i0000−i2i2i2−i2i2−i2−i2i22−2−22−222−2000000000000000000000000000000000000000000000000

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