Finite Group Databasebeta

← Group #10692273

Character table — Group #10692273

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212161616161616161616161616242424242424242424244848
order1222344444466624444444661212121212121212246612121212121212128888246688121224242424888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-11-1-111111111111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111-1-11-1-111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ71111111111111111-1-11-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1
χ81111111111111111-1-11-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111
χ91111111-1-1-1-11111-1111-1-1-111-1-1-1-11111-11-1-1-1-11111-1-1ii−i−i1-1111-1-1-111-1-1i−iii−i−iii−i−ii−i
χ101111111-1-1-1-11111-1111-1-1-111-1-1-1-11111-11-1-1-1-11111-1-1ii−i−i-11-1-1-1111-1-111i−iii−i−i−i−iii−ii
χ111111111-1-1-1-11111-1111-1-1-111-1-1-1-11111-11-1-1-1-11111-1-1−i−iii1-1111-1-1-111-1-1−ii−i−iii−i−iii−ii
χ121111111-1-1-1-11111-1111-1-1-111-1-1-1-11111-11-1-1-1-11111-1-1−i−iii-11-1-1-1111-1-111−ii−i−iiiii−i−ii−i
χ131111111-1-1-1-11111-1-1-1111-111-1-1-1-111111-111-1-1-1-1-1-111ii−i−i1-111-11-1-1-1-111i−i−i−iii−i−iiii−i
χ141111111-1-1-1-11111-1-1-1111-111-1-1-1-111111-111-1-1-1-1-1-111ii−i−i-11-1-11-11111-1-1i−i−i−iiiii−i−i−ii
χ151111111-1-1-1-11111-1-1-1111-111-1-1-1-111111-111-1-1-1-1-1-111−i−iii1-111-11-1-1-1-111−iiii−i−iii−i−i−ii
χ161111111-1-1-1-11111-1-1-1111-111-1-1-1-111111-111-1-1-1-1-1-111−i−iii-11-1-11-11111-1-1−iiii−i−i−i−iiii−i
χ17222222222-2-2222-2-222-2-2-22-2-222-2-22-2-222-2222-222-2-2-2-20000000000000000000000000000
χ18222222222-2-2222-2-2-2-2-2222-2-222-2-22-2-22-22-2-22-2-2-222220000000000000000000000000000
χ192222222-2-222222-2222-222-2-2-2-2-2222-2-22-2-2-2-2-2222-2-2220000000000000000000000000000
χ202222222-2-222222-22-2-2-2-2-2-2-2-2-2-2222-2-222222-22-2-222-2-20000000000000000000000000000
χ2122222-2-22222222-2-200200-2-2-22222-222-20000-2-20000002222000000000000-2-20000000000
χ2222222-2-22222222-2-200200-2-2-22222-222-20000-2-2000000-2-2-2-2000000000000220000000000
χ2322222-2-222-2-22222200-200-22222-2-2-2-2-2-20000-220000000000000000000000002i−2i2i−2i000000
χ2422222-2-222-2-22222200-200-22222-2-2-2-2-2-20000-22000000000000000000000000−2i2i−2i2i000000
χ2522222-2-2-2-2222222-200-200222-2-222-2-2-2-200002-20000000000000000000000002-2-22000000
χ2622222-2-2-2-2222222-200-200222-2-222-2-2-2-200002-2000000000000000000000000-222-2000000
χ2722222-2-2-2-2-2-2222-22002002-2-2-2-2-2-2-222-20000220000002i2i−2i−2i000000000000−2i2i0000000000
χ2822222-2-2-2-2-2-2222-22002002-2-2-2-2-2-2-222-2000022000000−2i−2i2i2i0000000000002i−2i0000000000
χ292222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000022-1-122-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-211-2-2111111000000000000
χ312222-1222222-1-1-122-2-22-2-22-1-1-1-1-1-1-1-1-1-1-2-211-1-1111111000022-1-1-2-2-1-11111000000000000
χ322222-1222222-1-1-122-2-22-2-22-1-1-1-1-1-1-1-1-1-1-2-211-1-11111110000-2-2112211-1-1-1-1000000000000
χ332222-12222-2-2-1-1-1-2-222-2-2-2211-1-111-111-12-2-1-1-11-1-11111000000−i3i300−i3i3−i3i3−i3i3000000000000
χ342222-12222-2-2-1-1-1-2-222-2-2-2211-1-111-111-12-2-1-1-11-1-11111000000i3−i300i3−i3i3−i3i3−i3000000000000
χ352222-12222-2-2-1-1-1-2-2-2-2-222211-1-111-111-1-2211-1111-1-1-1-1000000−i3i300−i3i3i3−i3i3−i3000000000000
χ362222-12222-2-2-1-1-1-2-2-2-2-222211-1-111-111-1-2211-1111-1-1-1-1000000i3−i300i3−i3−i3i3−i3i3000000000000
χ372222-122-2-222-1-1-1-2222-222-21111-1-1-111-1-2-2111-1-1-111-1-1000000−i3i300i3−i3−i3i3i3−i3000000000000
χ382222-122-2-222-1-1-1-2222-222-21111-1-1-111-1-2-2111-1-1-111-1-1000000i3−i300−i3i3i3−i3−i3i3000000000000
χ392222-122-2-222-1-1-1-22-2-2-2-2-2-21111-1-1-111-122-1-11-111-1-111000000−i3i300i3−i3i3−i3−i3i3000000000000
χ402222-122-2-222-1-1-1-22-2-2-2-2-2-21111-1-1-111-122-1-11-111-1-111000000i3−i300−i3i3−i3i3i3−i3000000000000
χ412222-122-2-2-2-2-1-1-12-2222-2-2-2-1-11111-1-1-1-1-221111-1-1-1-11100002-2-1-12-211-1-111000000000000
χ422222-122-2-2-2-2-1-1-12-2222-2-2-2-1-11111-1-1-1-1-221111-1-1-1-1110000-2211-22-1-111-1-1000000000000
χ432222-122-2-2-2-2-1-1-12-2-2-2222-2-1-11111-1-1-1-12-2-1-1111111-1-100002-2-1-1-221111-1-1000000000000
χ442222-122-2-2-2-2-1-1-12-2-2-2222-2-1-11111-1-1-1-12-2-1-1111111-1-10000-22112-2-1-1-1-111000000000000
χ454444-2-4-44444-2-2-2-4-400400-422-2-2-2-22-2-220000220000000000000000000000000000000000
χ464444-2-4-444-4-4-2-2-24400-400-4-2-2-2-222222200002-20000000000000000000000000000000000
χ474444-2-4-4-4-444-2-2-24-400-4004-2-222-2-222220000-220000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2-440040042222222-2-220000-2-20000000000000000000000000000000000
χ4944-4-4400004i−4i4-4-40000000000004i−4i000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ5044-4-4400004i−4i4-4-40000000000004i−4i00000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ5144-4-440000−4i4i4-4-4000000000000−4i4i00000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ5244-4-440000−4i4i4-4-4000000000000−4i4i000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ534-44-44004i−4i00-44-400000000004i−4i0000000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ544-44-44004i−4i00-44-400000000004i−4i000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ554-44-4400−4i4i00-44-40000000000−4i4i0000000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ564-44-4400−4i4i00-44-40000000000−4i4i000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ574-4-4444-40000-4-44004i−4i0000000000400-40000004i−4i00000000000000000000000000000000
χ584-4-4444-40000-4-4400−4i4i0000000000400-4000000−4i4i00000000000000000000000000000000
χ594-4-444-440000-4-44000004-40000000-400400000000004-40000000000000000000000000000
χ604-4-444-440000-4-4400000-440000000-40040000000000-440000000000000000000000000000
χ614-4-44-24-4000022-2004i−4i0000−2i32i30000-2−2i32i32000000−2i2i23−23000000000000000000000000000000
χ624-4-44-24-4000022-2004i−4i00002i3−2i30000-22i3−2i32000000−2i2i−2323000000000000000000000000000000
χ634-4-44-24-4000022-200−4i4i0000−2i32i30000-2−2i32i320000002i−2i−2323000000000000000000000000000000
χ644-4-44-24-4000022-200−4i4i00002i3−2i30000-22i3−2i320000002i−2i23−23000000000000000000000000000000
χ654-4-44-2-44000022-2000004-40−2i32i3000022i3−2i3-200−2i32i3000000-220000000000000000000000000000
χ664-4-44-2-44000022-2000004-402i3−2i300002−2i32i3-2002i3−2i3000000-220000000000000000000000000000
χ674-4-44-2-44000022-200000-440−2i32i3000022i3−2i3-2002i3−2i30000002-20000000000000000000000000000
χ684-4-44-2-44000022-200000-4402i3−2i300002−2i32i3-200−2i32i30000002-20000000000000000000000000000
χ6988-8-8-400008i−8i-444000000000000−4i4i00000000000000000000000000000000000000000000
χ7088-8-8-40000−8i8i-4440000000000004i−4i00000000000000000000000000000000000000000000
χ718-88-8-4008i−8i004-440000000000−4i4i0000000000000000000000000000000000000000000000
χ728-88-8-400−8i8i004-4400000000004i−4i0000000000000000000000000000000000000000000000

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