Finite Group Databasebeta

← Group #10691295

Character table — Group #10691295

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order1222444434444444466612121212248888888812121212121212128888888868888122424242424242424242424242424242422444444888824661212888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1
χ91111-1-1-1-1111-1-111-1-1111-1-1-1-1-11iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1ii−i−i1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i1-111-1-111-1-1i−i
χ101111-1-1-1-1111-1-111-1-1111-1-1-1-1-11iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1−i−iii1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i-11-1-111-1-111−ii
χ111111-1-1-1-1111-1-111-1-1111-1-1-1-1-11iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1ii−i−i1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii1-111-1-1-1-111−ii
χ121111-1-1-1-1111-1-111-1-1111-1-1-1-1-11iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1−i−iii1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-11-1-11111-1-1i−i
χ131111-1-1-1-1111-1-111-1-1111-1-1-1-1-11−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1ii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i-11-1-11111-1-1−ii
χ141111-1-1-1-1111-1-111-1-1111-1-1-1-1-11−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1−i−iii1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−i1-111-1-1-1-111i−i
χ151111-1-1-1-1111-1-111-1-1111-1-1-1-1-11−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1ii−i−i1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iii-11-1-111-1-111i−i
χ161111-1-1-1-1111-1-111-1-1111-1-1-1-1-11−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1−i−iii1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii1-111-1-111-1-1−ii
χ1722222222222-2-2-2-2222222222-2-20000000022-2-222-2-222222222-20000-2000000000000000000000000-2-2-2-2000000000000
χ1822222222222-2-2-2-2222222222-2-20000000022-2-222-2-2-2-2-2-2-2-2-2-2-20000-20000000000000000000000002222000000000000
χ19222222222-2-22222-2-22222222-2-200000000-2-222-2-22200000000-20000-2000000000000000022-2-2-2-2220000000000000000
χ20222222222-2-22222-2-22222222-2-200000000-2-222-2-22200000000-20000-20000000000000000-2-22222-2-20000000000000000
χ21222222222-2-2-2-2-2-2-2-22222222222i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-2-2-2000000002000022i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222222−2i−2i2i2i−2i−2i2i2i-2-2-2-2-2-2-2-200000000200002−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-2-2-2-2-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-12222-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-1-2-2-2-2-1111111111111111100000000000022-1-1-1-1000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i−2i−2i2i2i−2i−2i1111111100000000-10000-1−i−iii−i−iii33−3−333−3−300000000000000−i3i3−i3i3000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i−2i−2i2i2i−2i−2i1111111100000000-10000-1−i−iii−i−iii−3−333−3−33300000000000000i3−i3i3−i3000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i2i2i−2i−2i2i2i1111111100000000-10000-1ii−i−iii−i−i33−3−333−3−300000000000000i3−i3i3−i3000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i2i2i−2i−2i2i2i1111111100000000-10000-1ii−i−iii−i−i−3−333−3−33300000000000000−i3i3−i3i3000000
χ312222-2-2-2-222222-2-2-2-2222-2-2-2-22-20000000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i20000-2000000000000000000000000−2i−2i2i2i000000000000
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-22-20000000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i20000-20000000000000000000000002i2i−2i−2i000000000000
χ332222-2-2-2-22-2-222-2-222222-2-2-2-2-2222-2-2-2-222-2-2-2-2222200000000-20000222-2-2-2-22200000000000000000000000000000000
χ342222-2-2-2-22-2-222-2-222222-2-2-2-2-22-2-22222-2-2-2-2-2-2222200000000-200002-2-22222-2-200000000000000000000000000000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-22-200000000-2-22222-2-20000000020000-2000000000000000022-2-222-2-20000000000000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-22-200000000-2-22222-2-20000000020000-20000000000000000-2-222-2-2220000000000000000
χ372222-2-2-2-2-122-2-222-2-2-1-1-11111-222i2i2i2i−2i−2i−2i−2i-1-1-1-111110000000012i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
χ382222-2-2-2-2-122-2-222-2-2-1-1-11111-222i2i2i2i−2i−2i−2i−2i-1-1-1-11111000000001−2i−2i2i2i-1−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ392222-2-2-2-2-122-2-222-2-2-1-1-11111-22−2i−2i−2i−2i2i2i2i2i-1-1-1-111110000000012i2i−2i−2i-1iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
χ402222-2-2-2-2-122-2-222-2-2-1-1-11111-22−2i−2i−2i−2i2i2i2i2i-1-1-1-11111000000001−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
χ412222-2-2-2-2-1-2-222-2-222-1-1-11111-2222-2-2-2-2221111-1-1-1-10000000010000-1-1-11111-1-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i3000000
χ422222-2-2-2-2-1-2-222-2-222-1-1-11111-2222-2-2-2-2221111-1-1-1-10000000010000-1-1-11111-1-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i3000000
χ432222-2-2-2-2-1-2-222-2-222-1-1-11111-22-2-22222-2-21111-1-1-1-10000000010000-111-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i3000000
χ442222-2-2-2-2-1-2-222-2-222-1-1-11111-22-2-22222-2-21111-1-1-1-10000000010000-111-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i3000000
χ4522-2-22i−2i2i−2i2002i−2i2-2002-2-22i2i−2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i002-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002-200002i−2i1+i−1−i1−i−1+i000000000000
χ4622-2-22i−2i2i−2i2002i−2i2-2002-2-22i2i−2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i002-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000-220000−2i2i−1−i1+i−1+i1−i000000000000
χ4722-2-22i−2i2i−2i2002i−2i2-2002-2-22i2i−2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i002-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000-220000−2i2i1+i−1−i1−i−1+i000000000000
χ4822-2-22i−2i2i−2i2002i−2i2-2002-2-22i2i−2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i002-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000002-200002i−2i−1−i1+i−1+i1−i000000000000
χ4922-2-22i−2i2i−2i200−2i2i-22002-2-22i2i−2i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i00-2200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000002i−2i2-200−1−i1+i−1+i1−i000000000000
χ5022-2-22i−2i2i−2i200−2i2i-22002-2-22i2i−2i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i00-2200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000−2i2i-22001+i−1−i1−i−1+i000000000000
χ5122-2-22i−2i2i−2i200−2i2i-22002-2-22i2i−2i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i00-2200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000−2i2i-2200−1−i1+i−1+i1−i000000000000
χ5222-2-22i−2i2i−2i200−2i2i-22002-2-22i2i−2i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i00-2200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000002i−2i2-2001+i−1−i1−i−1+i000000000000
χ5322-2-2−2i2i−2i2i2002i−2i-22002-2-2−2i−2i2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i00-22002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000−2i2i2-200−1+i1−i−1−i1+i000000000000
χ5422-2-2−2i2i−2i2i2002i−2i-22002-2-2−2i−2i2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i00-22002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000002i−2i-22001−i−1+i1+i−1−i000000000000
χ5522-2-2−2i2i−2i2i2002i−2i-22002-2-2−2i−2i2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i00-22002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000002i−2i-2200−1+i1−i−1−i1+i000000000000
χ5622-2-2−2i2i−2i2i2002i−2i-22002-2-2−2i−2i2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i00-22002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000−2i2i2-2001−i−1+i1+i−1−i000000000000
χ5722-2-2−2i2i−2i2i200−2i2i2-2002-2-2−2i−2i2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i002-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000002-20000−2i2i1−i−1+i1+i−1−i000000000000
χ5822-2-2−2i2i−2i2i200−2i2i2-2002-2-2−2i−2i2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i002-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000-2200002i−2i−1+i1−i−1−i1+i000000000000
χ5922-2-2−2i2i−2i2i200−2i2i2-2002-2-2−2i−2i2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i002-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000-2200002i−2i1−i−1+i1+i−1−i000000000000
χ6022-2-2−2i2i−2i2i200−2i2i2-2002-2-2−2i−2i2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i002-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000002-20000−2i2i−1+i1−i−1−i1+i000000000000
χ612-22-22i−2i−2i2i22-200002i−2i-22-22i−2i2i−2i00000000002-2002i−2i00−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2301−i−1+i1+i−1−i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000002−2−i2i200
χ622-22-22i−2i−2i2i22-200002i−2i-22-22i−2i2i−2i00000000002-2002i−2i00−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230−1+i1−i−1−i1+i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000−22i2−i200
χ632-22-22i−2i−2i2i22-200002i−2i-22-22i−2i2i−2i00000000002-2002i−2i002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2301−i−1+i1+i−1−i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000−22i2−i200
χ642-22-22i−2i−2i2i22-200002i−2i-22-22i−2i2i−2i00000000002-2002i−2i002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230−1+i1−i−1−i1+i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000002−2−i2i200
χ652-22-2−2i2i2i−2i22-20000−2i2i-22-2−2i2i−2i2i00000000002-200−2i2i002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1301+i−1−i1−i−1+i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000002−2i2−i200
χ662-22-2−2i2i2i−2i22-20000−2i2i-22-2−2i2i−2i2i00000000002-200−2i2i002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130−1−i1+i−1+i1−i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000−22−i2i200
χ672-22-2−2i2i2i−2i22-20000−2i2i-22-2−2i2i−2i2i00000000002-200−2i2i00−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1301+i−1−i1−i−1+i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000−22−i2i200
χ682-22-2−2i2i2i−2i22-20000−2i2i-22-2−2i2i−2i2i00000000002-200−2i2i00−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130−1−i1+i−1+i1−i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000002−2i2−i200
χ6944444444-244-4-4-4-444-2-2-2-2-2-2-2-4-400000000-2-222-2-222000000002000020000000000000000000000000000000000000000
χ7044444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-40000000022-2-222-2-2000000002000020000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.