Finite Group Databasebeta

← Group #10692000

Character table — Group #10692000

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12223444444446662224444444412121212121212121212666121212121212128888888888888888246688121224242424888888
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
χ511111111111111111-1-11-1-1-1-11-1-111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1
χ611111111111111111-1-11-1-1-1-11-1-111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ711111111111111111-1-11-1-1-1-11-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111
χ811111111111111111-1-11-1-1-1-11-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1
χ91111111-1-1-1-1-1-1111-1111-1-1-1-1111-1-1-1-111-1-111-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i1-1111-1-1-111-1-1ii−i−ii−i
χ101111111-1-1-1-1-1-1111-1111-1-1-1-1111-1-1-1-111-1-111-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-11-1-1-1111-1-111−i−iii−ii
χ111111111-1-1-1-1-1-1111-1111-1-1-1-1111-1-1-1-111-1-111-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii1-1111-1-1-111-1-1−i−iii−ii
χ121111111-1-1-1-1-1-1111-1111-1-1-1-1111-1-1-1-111-1-111-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-11-1-1-1111-1-111ii−i−ii−i
χ131111111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1-111111-1-1iiii−i−i−i−i−i−i−i−iiiii1-111-11-1-1-1-111ii−i−i−ii
χ141111111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1-111111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-11-11111-1-1−i−iiii−i
χ151111111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1-111111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-111-11-1-1-1-111−i−iiii−i
χ161111111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1-111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-11-11111-1-1ii−i−i−ii
χ1722222222222-2-2222-222-222-2-2-2-2-222-2-2-2-22222-222-222-2-2-2-20000000000000000000000000000000000
χ1822222222222-2-2222-2-2-2-2-2-222-22222-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000000000
χ192222222-2-2-2-222222222-2-2-222-2-2-2-2-222-2-2-2-222222-2-2-222-2-20000000000000000000000000000000000
χ202222222-2-2-2-2222222-2-2-222-2-2-222-2-222-2-2-2-2222-2-2-222-2-2220000000000000000000000000000000000
χ2122222-2-222-2-222222-200-20000200222222-2-2-2-2-200-20000000000000022-2-222-2-2000000000000000000
χ2222222-2-222-2-222222-200-20000200222222-2-2-2-2-200-200000000000000-2-222-2-222000000000000000000
χ2322222-2-222-2-2-2-222220020000-20022-2-2-2-2-2-2-2-220020000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ2422222-2-222-2-2-2-222220020000-20022-2-2-2-2-2-2-2-22002000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ2522222-2-2-2-22222222-20020000-200-2-222-2-222-2-2-200200000022-2-2-2-22200000000000000000000000000
χ2622222-2-2-2-22222222-20020000-200-2-222-2-222-2-2-2002000000-2-22222-2-200000000000000000000000000
χ2722222-2-2-2-222-2-2222200-20000200-2-2-2-22222-2-2200-2000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222-2-2-2-222-2-2222200-20000200-2-2-2-22222-2-2200-200000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-122222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-122-1-1-1-1-1-1000000
χ302222-122222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-211-2-2111111000000
χ312222-122222222-1-1-12-2-22-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-111-1111111000000000000000022-1-1-2-2-1-11111000000
χ322222-122222222-1-1-12-2-22-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-111-11111110000000000000000-2-2112211-1-1-1-1000000
χ332222-1222222-2-2-1-1-1-222-222-2-2-2-2-2-1-11111-1-1-1-11-1-11-1-11111000000000000000000−i3i300−i3i3−i3i3−i3i3000000
χ342222-1222222-2-2-1-1-1-222-222-2-2-2-2-2-1-11111-1-1-1-11-1-11-1-11111000000000000000000i3−i300i3−i3i3−i3i3−i3000000
χ352222-1222222-2-2-1-1-1-2-2-2-2-2-222-222-1-11111-1-1-1-1111111-1-1-1-1000000000000000000−i3i300−i3i3i3−i3i3−i3000000
χ362222-1222222-2-2-1-1-1-2-2-2-2-2-222-222-1-11111-1-1-1-1111111-1-1-1-1000000000000000000i3−i300i3−i3−i3i3−i3i3000000
χ372222-122-2-2-2-222-1-1-1222-2-2-222-2-2-211-1-11111-1-1-1-1-1111-1-111000000000000000000−i3i300i3−i3−i3i3i3−i3000000
χ382222-122-2-2-2-222-1-1-1222-2-2-222-2-2-211-1-11111-1-1-1-1-1111-1-111000000000000000000i3−i300−i3i3i3−i3−i3i3000000
χ392222-122-2-2-2-222-1-1-12-2-2-222-2-2-22211-1-11111-1-1-1111-1-111-1-1000000000000000000−i3i300i3−i3i3−i3−i3i3000000
χ402222-122-2-2-2-222-1-1-12-2-2-222-2-2-22211-1-11111-1-1-1111-1-111-1-1000000000000000000i3−i300−i3i3−i3i3i3−i3000000
χ412222-122-2-2-2-2-2-2-1-1-1-2222-2-2-2-22221111-1-111-1-11-1-1-11111-1-100000000000000002-2-1-12-211-1-111000000
χ422222-122-2-2-2-2-2-2-1-1-1-2222-2-2-2-22221111-1-111-1-11-1-1-11111-1-10000000000000000-2211-22-1-111-1-1000000
χ432222-122-2-2-2-2-2-2-1-1-1-2-2-2222222-2-21111-1-111-1-1111-1-1-1-1-11100000000000000002-2-1-1-221111-1-1000000
χ442222-122-2-2-2-2-2-2-1-1-1-2-2-2222222-2-21111-1-111-1-1111-1-1-1-1-1110000000000000000-22112-2-1-1-1-111000000
χ4522-2-222-22i−2i2i−2i002-2-20000002-202i−2i2i−2i00002i−2i2-20000002-22i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4622-2-222-22i−2i2i−2i002-2-20000002-202i−2i2i−2i00002i−2i2-20000002-22i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4722-2-222-22i−2i2i−2i002-2-2000000-220−2i2i2i−2i00002i−2i2-2000000-22−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4822-2-222-22i−2i2i−2i002-2-2000000-220−2i2i2i−2i00002i−2i2-2000000-22−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4922-2-222-2−2i2i−2i2i002-2-20000002-20−2i2i−2i2i0000−2i2i2-20000002-2−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ5022-2-222-2−2i2i−2i2i002-2-20000002-20−2i2i−2i2i0000−2i2i2-20000002-2−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ5122-2-222-2−2i2i−2i2i002-2-2000000-2202i−2i−2i2i0000−2i2i2-2000000-222i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ5222-2-222-2−2i2i−2i2i002-2-2000000-2202i−2i−2i2i0000−2i2i2-2000000-222i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ5322-2-22-222i−2i−2i2i002-2-202-202i−2i000002i−2i0000−2i2i-2202-202i−2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ5422-2-22-222i−2i−2i2i002-2-202-202i−2i000002i−2i0000−2i2i-2202-202i−2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ5522-2-22-222i−2i−2i2i002-2-20-220−2i2i000002i−2i0000−2i2i-220-220−2i2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ5622-2-22-222i−2i−2i2i002-2-20-220−2i2i000002i−2i0000−2i2i-220-220−2i2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ5722-2-22-22−2i2i2i−2i002-2-202-20−2i2i00000−2i2i00002i−2i-2202-20−2i2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ5822-2-22-22−2i2i2i−2i002-2-202-20−2i2i00000−2i2i00002i−2i-2202-20−2i2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ5922-2-22-22−2i2i2i−2i002-2-20-2202i−2i00000−2i2i00002i−2i-220-2202i−2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ6022-2-22-22−2i2i2i−2i002-2-20-2202i−2i00000−2i2i00002i−2i-220-2202i−2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ614444-2-4-444-4-444-2-2-2-400-40000400-2-2-2-2-2-2222220020000000000000000000000000000000000000000
χ624444-2-4-444-4-4-4-4-2-2-240040000-400-2-222222222-200-20000000000000000000000000000000000000000
χ634444-2-4-4-4-44444-2-2-2-40040000-40022-2-222-2-222200-20000000000000000000000000000000000000000
χ644444-2-4-4-4-444-4-4-2-2-2400-400004002222-2-2-2-222-20020000000000000000000000000000000000000000
χ6544-4-4-24-44i−4i4i−4i00-2220000004-404i−4i−2i2i0000−2i2i-22000000-22−2i2i0000000000000000000000000000000000
χ6644-4-4-24-44i−4i4i−4i00-222000000-440−4i4i−2i2i0000−2i2i-220000002-22i−2i0000000000000000000000000000000000
χ6744-4-4-24-4−4i4i−4i4i00-2220000004-40−4i4i2i−2i00002i−2i-22000000-222i−2i0000000000000000000000000000000000
χ6844-4-4-24-4−4i4i−4i4i00-222000000-4404i−4i2i−2i00002i−2i-220000002-2−2i2i0000000000000000000000000000000000
χ6944-4-4-2-444i−4i−4i4i00-22204-404i−4i00000−2i2i00002i−2i2-20-220−2i2i00000000000000000000000000000000000000
χ7044-4-4-2-444i−4i−4i4i00-2220-440−4i4i00000−2i2i00002i−2i2-202-202i−2i00000000000000000000000000000000000000
χ7144-4-4-2-44−4i4i4i−4i00-22204-40−4i4i000002i−2i0000−2i2i2-20-2202i−2i00000000000000000000000000000000000000
χ7244-4-4-2-44−4i4i4i−4i00-2220-4404i−4i000002i−2i0000−2i2i2-202-20−2i2i00000000000000000000000000000000000000
χ734-44-440000004i−4i-44-400000000000004i−4i000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ744-44-440000004i−4i-44-400000000000004i−4i00000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ754-44-44000000−4i4i-44-40000000000000−4i4i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ764-44-44000000−4i4i-44-40000000000000−4i4i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ778-88-8-40000008i−8i4-440000000000000−4i4i00000000000000000000000000000000000000000000000000
χ788-88-8-4000000−8i8i4-4400000000000004i−4i00000000000000000000000000000000000000000000000000
χ798-8-88800000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-40000000044-4000000000000000−4i34i3000000000000000000000000000000000000000000000000
χ818-8-88-40000000044-40000000000000004i3−4i3000000000000000000000000000000000000000000000000

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