Finite Group Databasebeta

← Group #10692002

Character table — Group #10692002

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12223444444446662446688888888121212121212121212122424242424242424224444448888888844881212121224242424888888
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
χ5111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111
χ911111-1-1-1-111-1-1111-111-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−iii−i−i1-1
χ1011111-1-1-1-111-1-1111-111-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii−i−iii-11
χ1111111-1-1-1-111-1-1111-111-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i11-1-1ii−i−i−i−iii-11
χ1211111-1-1-1-111-1-1111-111-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-1-111−i−iiiii−i−i1-1
χ1311111-1-1-1-111-1-1111-111-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii−i−iii1-1
χ1411111-1-1-1-111-1-1111-111-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−iii−i−i-11
χ1511111-1-1-1-111-1-1111-111-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1−ii11-1-1−i−iiiii−i−i-11
χ1611111-1-1-1-111-1-1111-111-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11i−i-1-111ii−i−i−i−iii1-1
χ1722222222222-2-2222-2-2-2-2-200000000222222-2-2-2-20000000022-2-222-2-200000000000000000000000000
χ1822222222222-2-2222-2-2-2-2-200000000222222-2-2-2-200000000-2-222-2-22200000000000000000000000000
χ192222222-2-2-2-222222-22-2-2-222-2-222-2-2-2-2-2-222222-222-2-222-2-20000000000000000000000000000000000
χ202222222-2-2-2-222222-22-2-2-2-2-222-2-222-2-2-2-222222-2-2-222-2-2220000000000000000000000000000000000
χ212222222-2-2-2-2-2-22222-222200000000-2-2-2-222-2-2-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222222-2-2-2-2-2-22222-222200000000-2-2-2-222-2-2-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222-2-222-2-222222-2-22-2-20000000022-2-2-2-222-22000000000000000022-2-2-2-222000000000000000000
χ2422222-2-222-2-222222-2-22-2-20000000022-2-2-2-222-220000000000000000-2-22222-2-2000000000000000000
χ2522222-2-222-2-2-2-222222-2222i2i−2i−2i−2i−2i2i2i22-2-2-2-2-2-22-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ2622222-2-222-2-2-2-222222-222−2i−2i2i2i2i2i−2i−2i22-2-2-2-2-2-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ2722222-2-2-2-222222222-2-22200000000-2-222-2-222-2-20000000022-2-2-2-22200000000000000000000000000
χ2822222-2-2-2-222222222-2-22200000000-2-222-2-222-2-200000000-2-22222-2-200000000000000000000000000
χ292222-122222222-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ302222-122222222-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ312222-122222222-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ322222-122222222-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
χ332222-122-2-2-2-222-1-1-1-22-21122-2-222-2-21111-1-1-1-1-11-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ342222-122-2-2-2-222-1-1-1-22-21122-2-222-2-21111-1-1-1-1-11-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ352222-122-2-2-2-222-1-1-1-22-211-2-222-2-2221111-1-1-1-1-1111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ362222-122-2-2-2-222-1-1-1-22-211-2-222-2-2221111-1-1-1-1-1111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ372222-1-2-222-2-2-2-2-1-1-122-2-1-12i2i−2i−2i−2i−2i2i2i-1-1111111-11−i−iiiii−i−i00000000000000000000−i3i3i3−i33−3−33000000
χ382222-1-2-222-2-2-2-2-1-1-122-2-1-12i2i−2i−2i−2i−2i2i2i-1-1111111-11−i−iiiii−i−i00000000000000000000i3−i3−i3i3−333−3000000
χ392222-1-2-222-2-2-2-2-1-1-122-2-1-1−2i−2i2i2i2i2i−2i−2i-1-1111111-11ii−i−i−i−iii00000000000000000000−i3i3i3−i3−333−3000000
χ402222-1-2-222-2-2-2-2-1-1-122-2-1-1−2i−2i2i2i2i2i−2i−2i-1-1111111-11ii−i−i−i−iii00000000000000000000i3−i3−i3i33−3−33000000
χ412222-1-2-2-2-222-2-2-1-1-1-222112i2i2i2i−2i−2i−2i−2i11-1-11111-1-1−i−i−i−iiiii00000000000000002-22i−2i-1-111−i−iii000000
χ422222-1-2-2-2-222-2-2-1-1-1-222112i2i2i2i−2i−2i−2i−2i11-1-11111-1-1−i−i−i−iiiii0000000000000000-22−2i2i11-1-1ii−i−i000000
χ432222-1-2-2-2-222-2-2-1-1-1-22211−2i−2i−2i−2i2i2i2i2i11-1-11111-1-1iiii−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i000000
χ442222-1-2-2-2-222-2-2-1-1-1-22211−2i−2i−2i−2i2i2i2i2i11-1-11111-1-1iiii−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii000000
χ452-22-222i−2i2i−2i2-200-22-2000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2-22i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ462-22-222i−2i2i−2i2-200-22-2000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2-22i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ472-22-222i−2i2i−2i2-200-22-200000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2-22i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ482-22-222i−2i2i−2i2-200-22-200000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2-22i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ492-22-222i−2i−2i2i-2200-22-2000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−2i2i-222i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i2-2002i−2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ502-22-222i−2i−2i2i-2200-22-2000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−2i2i-222i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200−2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ512-22-222i−2i−2i2i-2200-22-200000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2i2i-222i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2-2002i−2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ522-22-222i−2i−2i2i-2200-22-200000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2i2i-222i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200−2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ532-22-22−2i2i2i−2i-2200-22-2000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2i−2i-22−2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i2-200−2i2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ542-22-22−2i2i2i−2i-2200-22-2000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2i−2i-22−2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i-22002i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000
χ552-22-22−2i2i2i−2i-2200-22-200000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2i−2i-22−2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2-200−2i2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000
χ562-22-22−2i2i2i−2i-2200-22-200000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2i−2i-22−2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-22002i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ572-22-22−2i2i−2i2i2-200-22-2000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i2-2−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i002i−2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ582-22-22−2i2i−2i2i2-200-22-2000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i2-2−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ592-22-22−2i2i−2i2i2-200-22-200000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i2-2−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002i−2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ602-22-22−2i2i−2i2i2-200-22-200000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i2-2−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ614444-2444444-4-4-2-2-2-4-4-42200000000-2-2-2-2-2-22222000000000000000000000000000000000000000000
χ624444-244-4-4-4-4-4-4-2-2-24-44-2-2000000002222-2-2222-2000000000000000000000000000000000000000000
χ634444-2-4-444-4-444-2-2-2-4-442200000000-2-22222-2-22-2000000000000000000000000000000000000000000
χ644444-2-4-4-4-44444-2-2-24-4-4-2-20000000022-2-222-2-222000000000000000000000000000000000000000000
χ654-44-4-24i−4i4i−4i4-4002-22000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i−2i2i-22−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000000000
χ664-44-4-24i−4i4i−4i4-4002-2200000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i−2i2i-22−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000000000
χ674-44-4-24i−4i−4i4i-44002-22000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i2i−2i2-2−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000000000000000000000
χ684-44-4-24i−4i−4i4i-44002-2200000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i2i−2i2-2−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000000000000000000000
χ694-44-4-2−4i4i4i−4i-44002-22000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i−2i2i2-22i−2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000000000000000000000
χ704-44-4-2−4i4i4i−4i-44002-2200000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i−2i2i2-22i−2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000000000000000000000
χ714-44-4-2−4i4i−4i4i4-4002-22000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i2i−2i-222i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000000000
χ724-44-4-2−4i4i−4i4i4-4002-2200000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i2i−2i-222i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000000000
χ734-4-4440000004i−4i-4-4400000000000000000004i−4i00000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ744-4-4440000004i−4i-4-4400000000000000000004i−4i000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ754-4-444000000−4i4i-4-440000000000000000000−4i4i000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ764-4-444000000−4i4i-4-440000000000000000000−4i4i00000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ7788-8-88000000008-8-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-400000000-444000−4i34i3000000000000000000000000000000000000000000000000000000000000
χ7988-8-8-400000000-4440004i3−4i3000000000000000000000000000000000000000000000000000000000000
χ808-8-88-40000008i−8i44-40000000000000000000−4i4i00000000000000000000000000000000000000000000
χ818-8-88-4000000−8i8i44-400000000000000000004i−4i00000000000000000000000000000000000000000000

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