Finite Group Databasebeta

← Group #10691301

Character table — Group #10691301

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order122244443444444446668888888812121212246688881212121212121212121224242424242424242424242424242424224444448888888824668812122424242488888888
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
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1
χ91111-1-1-1-111111-1-1-1-1111iiii−i−i−i−i-1-1-1-1-11-1-1ii−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i11-1-1ii−i−i
χ101111-1-1-1-111111-1-1-1-1111iiii−i−i−i−i-1-1-1-1-11-1-1ii−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii-1-111−i−iii
χ111111-1-1-1-111111-1-1-1-1111iiii−i−i−i−i-1-1-1-1-11-1-1ii−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-111i−i-1-1ii−i−i-1-111−i−iii
χ121111-1-1-1-111111-1-1-1-1111iiii−i−i−i−i-1-1-1-1-11-1-1ii−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1-1−ii11−i−iii11-1-1ii−i−i
χ131111-1-1-1-111111-1-1-1-1111−i−i−i−iiiii-1-1-1-1-11-1-1−i−iii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii11-1-1−i−iii
χ141111-1-1-1-111111-1-1-1-1111−i−i−i−iiiii-1-1-1-1-11-1-1−i−iii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i-1-111ii−i−i
χ151111-1-1-1-111111-1-1-1-1111−i−i−i−iiiii-1-1-1-1-11-1-1−i−iii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i1-111−ii-1-1−i−iii-1-111ii−i−i
χ161111-1-1-1-111111-1-1-1-1111−i−i−i−iiiii-1-1-1-1-11-1-1−i−iii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-11-1-1i−i11ii−i−i11-1-1−i−iii
χ1722222222222-2-2-2-222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ19222222222-2-22222-2-2222000000002222-2-2-2-20000-2-22222-2-2-2-2000000000000000022-2-2-2-2220000000000000000000000000000
χ20222222222-2-22222-2-2222000000002222-2-2-2-20000-2-22222-2-2-2-20000000000000000-2-22222-2-20000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222200000000222222220000-2-2-2-2-2-222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ22222222222-2-2-2-2-2-2-2-222200000000222222220000-2-2-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-122-1-1-1-1-1-100000000
χ2422222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-211-2-211111100000000
χ2522222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-1-1-2-2-1-1111100000000
χ2622222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2112211-1-1-1-100000000
χ2722222222-122-2-2-2-222-1-1-122222222-1-1-1-1-2-211-2-2-2-2-1-1111111-1-1-1-1-1-11111-1-1-1-11111000000000000000000−i3i300−i3i3−i3i3−i3i300000000
χ2822222222-122-2-2-2-222-1-1-122222222-1-1-1-1-2-211-2-2-2-2-1-1111111-1-1-1-1-1-11111-1-1-1-11111000000000000000000i3−i300i3−i3i3−i3i3−i300000000
χ2922222222-122-2-2-2-222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2112222-1-1111111-1-11111-1-1-1-11111-1-1-1-1000000000000000000−i3i300−i3i3i3−i3i3−i300000000
χ3022222222-122-2-2-2-222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2112222-1-1111111-1-11111-1-1-1-11111-1-1-1-1000000000000000000i3−i300i3−i3−i3i3−i3i300000000
χ312222-2-2-2-2222-2-222-2-22222i2i2i2i−2i−2i−2i−2i-2-2-2-22-222−2i−2i2i2i22-2-222-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ322222-2-2-2-2222-2-222-2-2222−2i−2i−2i−2i2i2i2i2i-2-2-2-22-2222i2i−2i−2i22-2-222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ332222-2-2-2-22-2-222-2-22222200000000-2-2-2-22-2220000-2-222-2-2-2-222000000000000000022-2-222-2-20000000000000000000000000000
χ342222-2-2-2-22-2-222-2-22222200000000-2-2-2-22-2220000-2-222-2-2-2-2220000000000000000-2-222-2-2220000000000000000000000000000
χ352222-2-2-2-22-2-2-2-2222222200000000-2-2-2-2-22-2-20000-2-2-2-222222200000000000000000000000022-2-2-2-22200000000000000000000
χ362222-2-2-2-22-2-2-2-2222222200000000-2-2-2-2-22-2-20000-2-2-2-2222222000000000000000000000000-2-22222-2-200000000000000000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-12i2i2i2i−2i−2i−2i−2i1111-22112i2i−2i−2i-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-2-1-12i−2i11−i−iii00000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-12i2i2i2i−2i−2i−2i−2i1111-22112i2i−2i−2i-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-2211−2i2i-1-1ii−i−i00000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i1111-2211−2i−2i2i2i-1-1-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2-1-1−2i2i11ii−i−i00000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i1111-2211−2i−2i2i2i-1-1-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-22112i−2i-1-1−i−iii00000000
χ412222-2-2-2-2-122-2-222-2-2-1-1-12i2i2i2i−2i−2i−2i−2i11112-2-1-1−2i−2i2i2i-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i000000000000000000−i3i300i3−i33−3−3300000000
χ422222-2-2-2-2-122-2-222-2-2-1-1-12i2i2i2i−2i−2i−2i−2i11112-2-1-1−2i−2i2i2i-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i000000000000000000i3−i300−i3i3−333−300000000
χ432222-2-2-2-2-122-2-222-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i11112-2-1-12i2i−2i−2i-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii000000000000000000−i3i300i3−i3−333−300000000
χ442222-2-2-2-2-122-2-222-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i11112-2-1-12i2i−2i−2i-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii000000000000000000i3−i300−i3i33−3−3300000000
χ4522-2-22i−2i2i−2i2002-22i−2i002-2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i00001+i−1−i1−i−1+i002-22i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002i−2i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ4622-2-22i−2i2i−2i2002-22i−2i002-2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i00001+i−1−i1−i−1+i002-22i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00−2i2i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ4722-2-22i−2i2i−2i2002-22i−2i002-2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i0000−1−i1+i−1+i1−i002-22i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002i−2i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ4822-2-22i−2i2i−2i2002-22i−2i002-2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i0000−1−i1+i−1+i1−i002-22i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00−2i2i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ4922-2-22i−2i2i−2i200-22−2i2i002-2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i0000−1−i1+i−1+i1−i00-22−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i2-200002i−2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000000000
χ5022-2-22i−2i2i−2i200-22−2i2i002-2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i0000−1−i1+i−1+i1−i00-22−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i-220000−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000000000
χ5122-2-22i−2i2i−2i200-22−2i2i002-2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i00001+i−1−i1−i−1+i00-22−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i2-200002i−2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000000000
χ5222-2-22i−2i2i−2i200-22−2i2i002-2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i00001+i−1−i1−i−1+i00-22−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i-220000−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000000000
χ5322-2-2−2i2i−2i2i2002-2−2i2i002-2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i00001−i−1+i1+i−1−i002-2−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i002i−2i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ5422-2-2−2i2i−2i2i2002-2−2i2i002-2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i00001−i−1+i1+i−1−i002-2−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00−2i2i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ5522-2-2−2i2i−2i2i2002-2−2i2i002-2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i0000−1+i1−i−1−i1+i002-2−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i002i−2i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ5622-2-2−2i2i−2i2i2002-2−2i2i002-2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i0000−1+i1−i−1−i1+i002-2−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00−2i2i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ5722-2-2−2i2i−2i2i200-222i−2i002-2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i0000−1+i1−i−1−i1+i00-222i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i2-20000−2i2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000000000
χ5822-2-2−2i2i−2i2i200-222i−2i002-2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i0000−1+i1−i−1−i1+i00-222i−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-2200002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000000000
χ5922-2-2−2i2i−2i2i200-222i−2i002-2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i00001−i−1+i1+i−1−i00-222i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i2-20000−2i2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000000000
χ6022-2-2−2i2i−2i2i200-222i−2i002-2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i00001−i−1+i1+i−1−i00-222i−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-2200002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000000000
χ612-22-22i−2i−2i2i22-200002i−2i-22-2−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232i−2i−2i2i000000002-20000002i−2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000002−2−i2i21−i−1+i1+i−1−i
χ622-22-22i−2i−2i2i22-200002i−2i-22-2−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232i−2i−2i2i000000002-20000002i−2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000−22i2−i2−1+i1−i−1−i1+i
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.