Finite Group Databasebeta

← Group #10693609

Character table — Group #10693609

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order122244442234444444444444466612121212444444661212121212121212121212121212121212121212121212121212888888888888888824668812122424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1
χ91111-1-1-1-1-1-111iiii−i−i−i−i11-1-11111-1-1-1-11-1ii−i−i-1-11111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-111i−i-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1-1-111iiii−i−i−i−i11-1-11111-1-1-1-11-1ii−i−i-1-11111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11-1-1−ii11−i−iii−i−iii-1-111
χ111111-1-1-1-1-1-111iiii−i−i−i−i11-1-11111-1-1-1-11-1ii−i−i-1-11111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-111111-111i−i-1-1ii−i−i−i−iii-1-111
χ121111-1-1-1-1-1-111iiii−i−i−i−i11-1-11111-1-1-1-11-1ii−i−i-1-11111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11-1-1−ii11−i−iiiii−i−i11-1-1
χ131111-1-1-1-1-1-111−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−iii-1-11111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-111111-111−ii-1-1−i−iiiii−i−i-1-111
χ141111-1-1-1-1-1-111−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−iii-1-11111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111-11-1-1i−i11ii−i−i−i−iii11-1-1
χ151111-1-1-1-1-1-111−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−iii-1-11111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-11-111−ii-1-1−i−iii−i−iii11-1-1
χ161111-1-1-1-1-1-111−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−iii-1-11111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1-11-1-1i−i11ii−i−iii−i−i-1-111
χ1722222222222222222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ192222222222-122222222222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-122-1-1-1-1-1-100000000
χ202222222222-122222222222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-211-2-211111100000000
χ212222222222-1222222222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-2-2-2-1-111111111-1-1-1-1-1-11111-1-1-1-11111000000000000000000−i3i300−i3i3−i3i3−i3i300000000
χ222222222222-1222222222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-2-2-2-1-111111111-1-1-1-1-1-11111-1-1-1-11111000000000000000000i3−i300i3−i3i3−i3i3−i300000000
χ232222222222-12-2-2-2-2-2-2-2-222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-1-1-2-2-1-1111100000000
χ242222222222-12-2-2-2-2-2-2-2-222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2112211-1-1-1-100000000
χ252222222222-12-2-2-2-2-2-2-2-2-2-2-2-22-1-1-1-1-1-1-1-2-22222-1-111111111-1-11111-1-1-1-11111-1-1-1-1000000000000000000−i3i300−i3i3i3−i3i3−i300000000
χ262222222222-12-2-2-2-2-2-2-2-2-2-2-2-22-1-1-1-1-1-1-1-2-22222-1-111111111-1-11111-1-1-1-11111-1-1-1-1000000000000000000i3−i300i3−i3−i3i3−i3i300000000
χ2722222222-2-22-2000000002222-22222222-2-20000-2-222-2-222-2-2-2-2000000000000000022-2-222-2-20000000000000000000000000000
χ2822222222-2-22-2000000002222-22222222-2-20000-2-222-2-222-2-2-2-20000000000000000-2-222-2-2220000000000000000000000000000
χ2922222222-2-22-200000000-2-2-2-2-22222222220000-2-2-2-222-2-222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ3022222222-2-22-200000000-2-2-2-2-22222222220000-2-2-2-222-2-222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ312222-2-2-2-2222-20000000022-2-2-2222-2-2-2-2-2200002222-2-2-2-222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ322222-2-2-2-2222-20000000022-2-2-2222-2-2-2-2-2200002222-2-2-2-222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ332222-2-2-2-2222-200000000-2-222-2222-2-2-2-22-2000022-2-22222-2-2-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ342222-2-2-2-2222-200000000-2-222-2222-2-2-2-22-2000022-2-22222-2-2-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ352222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-2222222-2-2-2-2-22−2i−2i2i2i-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ362222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-2222222-2-2-2-2-222i2i−2i−2i-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i22-2-22-1-1-111112-22i2i−2i−2i11-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-2-1-12i−2i11−i−iii00000000
χ382222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i22-2-22-1-1-111112-22i2i−2i−2i11-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-2211−2i2i-1-1ii−i−i00000000
χ392222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i-2-2222-1-1-11111-22−2i−2i2i2i111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000000000−i3i300i3−i33−3−3300000000
χ402222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i-2-2222-1-1-11111-22−2i−2i2i2i111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000000000i3−i300−i3i3−333−300000000
χ412222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i22-2-22-1-1-111112-2−2i−2i2i2i11-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2-1-1−2i2i11ii−i−i00000000
χ422222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i22-2-22-1-1-111112-2−2i−2i2i2i11-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-22112i−2i-1-1−i−iii00000000
χ432222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i-2-2222-1-1-11111-222i2i−2i−2i111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000000000−i3i300i3−i3−333−300000000
χ442222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i-2-2222-1-1-11111-222i2i−2i−2i111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000000000i3−i300−i3i33−3−3300000000
χ4522-2-22i−2i2i−2i00201+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i02-2-22i−2i2i−2i001+i−1−i1−i−1+i002-2002i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−i2i2−i2i22−22−200000000000000000000
χ4622-2-22i−2i2i−2i00201+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i02-2-22i−2i2i−2i001+i−1−i1−i−1+i002-2002i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23i2−i2i2−i2−22−2200000000000000000000
χ4722-2-22i−2i2i−2i00201+i1+i−1−i−1−i1−i1−i−1+i−1+i-22−2i2i02-2-22i−2i2i−2i00−1−i1+i−1+i1−i00-2200−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13002−2−22i2−i2−i2i200000000000000000000
χ4822-2-22i−2i2i−2i00201+i1+i−1−i−1−i1−i1−i−1+i−1+i-22−2i2i02-2-22i−2i2i−2i00−1−i1+i−1+i1−i00-2200−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−222−2−i2i2i2−i200000000000000000000
χ4922-2-22i−2i2i−2i0020−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i02-2-22i−2i2i−2i00−1−i1+i−1+i1−i002-2002i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23i2−i2i2−i2−22−2200000000000000000000
χ5022-2-22i−2i2i−2i0020−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i02-2-22i−2i2i−2i00−1−i1+i−1+i1−i002-2002i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−i2i2−i2i22−22−200000000000000000000
χ5122-2-22i−2i2i−2i0020−1−i−1−i1+i1+i−1+i−1+i1−i1−i-22−2i2i02-2-22i−2i2i−2i001+i−1−i1−i−1+i00-2200−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−222−2−i2i2i2−i200000000000000000000
χ5222-2-22i−2i2i−2i0020−1−i−1−i1+i1+i−1+i−1+i1−i1−i-22−2i2i02-2-22i−2i2i−2i001+i−1−i1−i−1+i00-2200−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13002−2−22i2−i2−i2i200000000000000000000
χ5322-2-2−2i2i−2i2i00201−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i02-2-2−2i2i−2i2i001−i−1+i1+i−1−i002-200−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13i2−i2i2−i22−22−200000000000000000000
χ5422-2-2−2i2i−2i2i00201−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i02-2-2−2i2i−2i2i001−i−1+i1+i−1−i002-200−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−i2i2−i2i2−22−2200000000000000000000
χ5522-2-2−2i2i−2i2i00201−i1−i−1+i−1+i1+i1+i−1−i−1−i-222i−2i02-2-2−2i2i−2i2i00−1+i1−i−1−i1+i00-22002i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23002−2−22−i2i2i2−i200000000000000000000
χ5622-2-2−2i2i−2i2i00201−i1−i−1+i−1+i1+i1+i−1−i−1−i-222i−2i02-2-2−2i2i−2i2i00−1+i1−i−1−i1+i00-22002i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300−222−2i2−i2−i2i200000000000000000000
χ5722-2-2−2i2i−2i2i0020−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i02-2-2−2i2i−2i2i00−1+i1−i−1−i1+i002-200−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−i2i2−i2i2−22−2200000000000000000000
χ5822-2-2−2i2i−2i2i0020−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i02-2-2−2i2i−2i2i00−1+i1−i−1−i1+i002-200−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13i2−i2i2−i22−22−200000000000000000000
χ5922-2-2−2i2i−2i2i0020−1+i−1+i1−i1−i−1−i−1−i1+i1+i-222i−2i02-2-2−2i2i−2i2i001−i−1+i1+i−1−i00-22002i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300−222−2i2−i2−i2i200000000000000000000
χ6022-2-2−2i2i−2i2i0020−1+i−1+i1−i1−i−1−i−1−i1+i1+i-222i−2i02-2-2−2i2i−2i2i001−i−1+i1+i−1−i00-22002i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23002−2−22−i2i2i2−i200000000000000000000
χ612-2-2222-2-22-22-22i−2i2i−2i2i−2i2i−2i00002-2-2222-2-20000002-2000000002-22i−2i2i−2i00002i−2i2i−2i00000000000000000000000000000000−i2i2−i2i22−22−2
χ622-2-2222-2-22-22-22i−2i2i−2i2i−2i2i−2i00002-2-2222-2-20000002-2000000002-22i−2i2i−2i00002i−2i2i−2i00000000000000000000000000000000i2−i2i2−i2−22−22
χ632-2-2222-2-22-22-2−2i2i−2i2i−2i2i−2i2i00002-2-2222-2-20000002-2000000002-2−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000000000−i2i2−i2i2−22−22
χ642-2-2222-2-22-22-2−2i2i−2i2i−2i2i−2i2i00002-2-2222-2-20000002-2000000002-2−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000000000i2−i2i2−i22−22−2
χ652-2-22-2-222-222-22-22-2-22-2200002-2-22-2-222000000-22000000002-22-22-20000-22-22000000000000000000000000000000002−2−22−222−2
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.