Finite Group Databasebeta

← Group #10692007

Character table — Group #10692007

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order1222344444444666222444444441212121212121212121266612121212121212888888888888888844881212121224242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-11-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ611111111111111111-1-11-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ711111111111111111-1-11-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111-1-11-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ91111111-1-1-1-1-1-1111-1111111-1-1-1-111-1-1-1-1-1-111-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1ii−i−ii−i
χ101111111-1-1-1-1-1-1111-1111111-1-1-1-111-1-1-1-1-1-111-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−i−iii−ii
χ111111111-1-1-1-1-1-1111-1111111-1-1-1-111-1-1-1-1-1-111-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−ii
χ121111111-1-1-1-1-1-1111-1111111-1-1-1-111-1-1-1-1-1-111-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111ii−i−ii−i
χ131111111-1-1-1-1-1-1111-1-1-11-1-11111111-1-1-1-1-1-111-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111ii−i−i−ii
χ141111111-1-1-1-1-1-1111-1-1-11-1-11111111-1-1-1-1-1-111-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−i−iiii−i
χ151111111-1-1-1-1-1-1111-1-1-11-1-11111111-1-1-1-1-1-111-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−i−iiii−i
χ161111111-1-1-1-1-1-1111-1-1-11-1-11111111-1-1-1-1-1-111-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1ii−i−i−ii
χ1722222222222-2-2222-222-2-2-2-222-2-2-2-22222-2-222-222-2-2-222-2-20000000000000000000000000000000000
χ1822222222222-2-2222-2-2-2-222-2-2-222-2-22222-2-222-2-2-222-2-2-2220000000000000000000000000000000000
χ192222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-2-2-22222222-2-2-2-2-2220000000000000000000000000000000000
χ202222222-2-2-2-2222222-2-2-222-222-2-2-2-2-2-2-2-222222-2-222-222-2-20000000000000000000000000000000000
χ2122222-2-222-2-222222-200-20020000-2-222-2-222-2-2-200002000022-2-222-2-200000000000000000000000000
χ2222222-2-222-2-222222-200-20020000-2-222-2-222-2-2-2000020000-2-222-2-22200000000000000000000000000
χ2322222-2-222-2-2-2-2222200200-200002222-2-2-2-2-2-220000-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ2422222-2-222-2-2-2-2222200200-200002222-2-2-2-2-2-220000-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2522222-2-2-2-22222222-200200-2000022-2-22222-2-2-20000-200000000000022-2-2-2-222000000000000000000
χ2622222-2-2-2-22222222-200200-2000022-2-22222-2-2-20000-2000000000000-2-22222-2-2000000000000000000
χ2722222-2-2-2-222-2-2222200-20020000-2-2-2-222-2-2-2-220000200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2822222-2-2-2-222-2-2222200-20020000-2-2-2-222-2-2-2-22000020000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ292222-122222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ302222-122222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ312222-122222222-1-1-12-2-22-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111-11111000000000000000022-2-2-1-1-1-11111000000
χ322222-122222222-1-1-12-2-22-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111-111110000000000000000-2-2221111-1-1-1-1000000
χ332222-1222222-2-2-1-1-1-222-2-2-2-222-2-211-1-1-1-111-1-11-1-1111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ342222-1222222-2-2-1-1-1-222-2-2-2-222-2-211-1-1-1-111-1-11-1-1111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ352222-1222222-2-2-1-1-1-2-2-2-222-2-2-22211-1-1-1-111-1-1111-1-1111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ362222-1222222-2-2-1-1-1-2-2-2-222-2-2-22211-1-1-1-111-1-1111-1-1111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ372222-122-2-2-2-222-1-1-1222-2-2-2-2-2-222111111-1-1-1-1-1-1-111111-1-100000000000000000000−i3i3i3−i3−i3i3i3−i3000000
χ382222-122-2-2-2-222-1-1-1222-2-2-2-2-2-222111111-1-1-1-1-1-1-111111-1-100000000000000000000i3−i3−i3i3i3−i3−i3i3000000
χ392222-122-2-2-2-222-1-1-12-2-2-222-222-2-2111111-1-1-1-1-111-1-11-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i3000000
χ402222-122-2-2-2-222-1-1-12-2-2-222-222-2-2111111-1-1-1-1-111-1-11-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i3000000
χ412222-122-2-2-2-2-2-2-1-1-1-2222222-2-2-2-2-1-1111111-1-11-1-1-1-1-1111100000000000000002-22-2-1-111-1-111000000
χ422222-122-2-2-2-2-2-2-1-1-1-2222222-2-2-2-2-1-1111111-1-11-1-1-1-1-111110000000000000000-22-2211-1-111-1-1000000
χ432222-122-2-2-2-2-2-2-1-1-1-2-2-22-2-222222-1-1111111-1-111111-1-1-1-1-100000000000000002-2-22-1-11111-1-1000000
χ442222-122-2-2-2-2-2-2-1-1-1-2-2-22-2-222222-1-1111111-1-111111-1-1-1-1-10000000000000000-222-211-1-1-1-111000000
χ452-22-222-22i−2i2i−2i00-22-200002i−2i0002-2002i−2i2i−2i002-20002i−2i0002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ462-22-222-22i−2i2i−2i00-22-200002i−2i0002-2002i−2i2i−2i002-20002i−2i0002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ472-22-222-22i−2i2i−2i00-22-20000−2i2i000-22002i−2i2i−2i002-2000−2i2i000-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ482-22-222-22i−2i2i−2i00-22-20000−2i2i000-22002i−2i2i−2i002-2000−2i2i000-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ492-22-222-2−2i2i−2i2i00-22-200002i−2i000-2200−2i2i−2i2i002-20002i−2i000-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ502-22-222-2−2i2i−2i2i00-22-200002i−2i000-2200−2i2i−2i2i002-20002i−2i000-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ512-22-222-2−2i2i−2i2i00-22-20000−2i2i0002-200−2i2i−2i2i002-2000−2i2i0002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ522-22-222-2−2i2i−2i2i00-22-20000−2i2i0002-200−2i2i−2i2i002-2000−2i2i0002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ532-22-22-222i−2i−2i2i00-22-202-200002i−2i00002i−2i−2i2i00-2202-20002i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ542-22-22-222i−2i−2i2i00-22-202-200002i−2i00002i−2i−2i2i00-2202-20002i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ552-22-22-222i−2i−2i2i00-22-20-220000−2i2i00002i−2i−2i2i00-220-22000−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ562-22-22-222i−2i−2i2i00-22-20-220000−2i2i00002i−2i−2i2i00-220-22000−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ572-22-22-22−2i2i2i−2i00-22-202-20000−2i2i0000−2i2i2i−2i00-2202-2000−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ582-22-22-22−2i2i2i−2i00-22-202-20000−2i2i0000−2i2i2i−2i00-2202-2000−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000
χ592-22-22-22−2i2i2i−2i00-22-20-2200002i−2i0000−2i2i2i−2i00-220-220002i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000
χ602-22-22-22−2i2i2i−2i00-22-20-2200002i−2i0000−2i2i2i−2i00-220-220002i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ614444-2-4-444-4-444-2-2-2-400-4004000022-2-222-2-22220000-200000000000000000000000000000000000000
χ624444-2-4-444-4-4-4-4-2-2-2400400-40000-2-2-2-2222222-20000200000000000000000000000000000000000000
χ634444-2-4-4-4-44444-2-2-2-400400-40000-2-222-2-2-2-22220000200000000000000000000000000000000000000
χ644444-2-4-4-4-444-4-4-2-2-2400-400400002222-2-22222-20000-200000000000000000000000000000000000000
χ654-44-4-24-44i−4i4i−4i002-2200004i−4i0004-400−2i2i−2i2i00-22000−2i2i000-220000000000000000000000000000000000
χ664-44-4-24-44i−4i4i−4i002-220000−4i4i000-4400−2i2i−2i2i00-220002i−2i0002-20000000000000000000000000000000000
χ674-44-4-24-4−4i4i−4i4i002-2200004i−4i000-44002i−2i2i−2i00-22000−2i2i0002-20000000000000000000000000000000000
χ684-44-4-24-4−4i4i−4i4i002-220000−4i4i0004-4002i−2i2i−2i00-220002i−2i000-220000000000000000000000000000000000
χ694-44-4-2-444i−4i−4i4i002-2204-400004i−4i0000−2i2i2i−2i002-20-22000−2i2i000000000000000000000000000000000000
χ704-44-4-2-444i−4i−4i4i002-220-440000−4i4i0000−2i2i2i−2i002-202-20002i−2i000000000000000000000000000000000000
χ714-44-4-2-44−4i4i4i−4i002-2204-40000−4i4i00002i−2i−2i2i002-20-220002i−2i000000000000000000000000000000000000
χ724-44-4-2-44−4i4i4i−4i002-220-4400004i−4i00002i−2i−2i2i002-202-2000−2i2i000000000000000000000000000000000000
χ734-4-4440000004i−4i-4-44000000000000000004i−4i0000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ744-4-4440000004i−4i-4-44000000000000000004i−4i00000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ754-4-444000000−4i4i-4-4400000000000000000−4i4i00000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ764-4-444000000−4i4i-4-4400000000000000000−4i4i0000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ7788-8-88000000008-8-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-400000000-44400000000000−4i34i30000000000000000000000000000000000000000000000000000
χ7988-8-8-400000000-444000000000004i3−4i30000000000000000000000000000000000000000000000000000
χ808-8-88-40000008i−8i44-400000000000000000−4i4i0000000000000000000000000000000000000000000000
χ818-8-88-4000000−8i8i44-4000000000000000004i−4i0000000000000000000000000000000000000000000000

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