Finite Group Databasebeta

← Group #10692280

Character table — Group #10692280

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212161616161616161616161616242424242424242424244848
order122234444446662224444466121212121212121244661212121212121212888844881212121224242424888888888888
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
χ5111111111111111-1-111-1-111111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ6111111111111111-1-111-1-111111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ7111111111111111-1-111-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1
χ8111111111111111-1-111-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111
χ91111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-11111-1-1-1-1-1-1ii−i−i1-11-111-1-111-1-1i−iii−i−iii−i−ii−i
χ101111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-11111-1-1-1-1-1-1ii−i−i-11-11-1-111-1-111i−iii−i−i−i−iii−ii
χ111111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-11111-1-1-1-1-1-1−i−iii1-11-111-1-111-1-1−ii−i−iii−i−iii−ii
χ121111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-11111-1-1-1-1-1-1−i−iii-11-11-1-111-1-111−ii−i−iiiii−i−ii−i
χ131111111-1-1-1-11111-1-11-111-111111-1-1-1-11-11-1-1-1-1-1-11111ii−i−i1-1-1111-1-1-1-111i−i−i−iii−i−iiii−i
χ141111111-1-1-1-11111-1-11-111-111111-1-1-1-11-11-1-1-1-1-1-11111ii−i−i-111-1-1-11111-1-1i−i−i−iiiii−i−i−ii
χ151111111-1-1-1-11111-1-11-111-111111-1-1-1-11-11-1-1-1-1-1-11111−i−iii1-1-1111-1-1-1-111−iiii−i−iii−i−i−ii
χ161111111-1-1-1-11111-1-11-111-111111-1-1-1-11-11-1-1-1-1-1-11111−i−iii-111-1-1-11111-1-1−iiii−i−i−i−iiii−i
χ17222222222-2-2222-222-2-2-2-22-2-22-2-222-2-22-2222-2-22-222-2-20000000000000000000000000000
χ18222222222-2-2222-2-2-2-2-2222-2-22-2-222-2-222-2-2-2222-2-2-2220000000000000000000000000000
χ192222222-2-222222-222-2222-2-2-22-2-2-2-2222-2-222-2-2-22-2-2220000000000000000000000000000
χ202222222-2-222222-2-2-2-22-2-2-2-2-22-2-2-2-222222-2-222-2222-2-20000000000000000000000000000
χ2122222-2-22222222-2002-200-2-2-2-2222222-2000000-2-200002222000000000000-2-20000000000
χ2222222-2-22222222-2002-200-2-2-2-2222222-2000000-2-20000-2-2-2-2000000000000220000000000
χ2322222-2-222-2-2222200-2200-222-2-2-222-2-2-2000000-2200000000000000000000002i−2i2i−2i000000
χ2422222-2-222-2-2222200-2200-222-2-2-222-2-2-2000000-220000000000000000000000−2i2i−2i2i000000
χ2522222-2-2-2-222222200-2-200222-2-2-2-2-222-20000002-200000000000000000000002-2-22000000
χ2622222-2-2-2-222222200-2-200222-2-2-2-2-222-20000002-20000000000000000000000-222-2000000
χ2722222-2-2-2-2-2-2222-20022002-2-2-222-2-2-2-2-20000002200002i2i−2i−2i000000000000−2i2i0000000000
χ2822222-2-2-2-2-2-2222-20022002-2-2-222-2-2-2-2-2000000220000−2i−2i2i2i0000000000002i−2i0000000000
χ292222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-211111111000000000000
χ312222-1222222-1-1-12-2-222-2-22-1-1-1-1-1-1-1-1-1-1-2-21111-1-11111000022-2-2-1-1-1-11111000000000000
χ322222-1222222-1-1-12-2-222-2-22-1-1-1-1-1-1-1-1-1-1-2-21111-1-111110000-2-2221111-1-1-1-1000000000000
χ332222-12222-2-2-1-1-1-222-2-2-2-2211-111-1-111-1-22-1-111-11-1-11100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ342222-12222-2-2-1-1-1-222-2-2-2-2211-111-1-111-1-22-1-111-11-1-11100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ352222-12222-2-2-1-1-1-2-2-2-2-222211-111-1-111-12-211-1-1-1111-1-100000000−i3i3−i3i3i3−i3i3−i3000000000000
χ362222-12222-2-2-1-1-1-2-2-2-2-222211-111-1-111-12-211-1-1-1111-1-100000000i3−i3i3−i3−i3i3−i3i3000000000000
χ372222-122-2-222-1-1-1-222-2222-211-11111-1-1-1-2-2-1-1111-111-1-100000000−i3i3i3−i3−i3i3i3−i3000000000000
χ382222-122-2-222-1-1-1-222-2222-211-11111-1-1-1-2-2-1-1111-111-1-100000000i3−i3−i3i3i3−i3−i3i3000000000000
χ392222-122-2-222-1-1-1-2-2-2-22-2-2-211-11111-1-1-12211-1-11-1-1-11100000000−i3i3i3−i3i3−i3−i3i3000000000000
χ402222-122-2-222-1-1-1-2-2-2-22-2-2-211-11111-1-1-12211-1-11-1-1-11100000000i3−i3−i3i3−i3i3i3−i3000000000000
χ412222-122-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-1-11111-12-2-1-1-1-111111100002-22-2-1-111-1-111000000000000
χ422222-122-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-1-11111-12-2-1-1-1-11111110000-22-2211-1-111-1-1000000000000
χ432222-122-2-2-2-2-1-1-12-2-22-222-2-1-1-1-1-11111-1-22111111-1-1-1-100002-2-22-1-11111-1-1000000000000
χ442222-122-2-2-2-2-1-1-12-2-22-222-2-1-1-1-1-11111-1-22111111-1-1-1-10000-222-211-1-1-1-111000000000000
χ454444-2-4-44444-2-2-2-4004-400-4222-2-2-2-2-2-220000002200000000000000000000000000000000
χ464444-2-4-444-4-4-2-2-2400-4400-4-2-2222-2-22220000002-200000000000000000000000000000000
χ474444-2-4-4-4-444-2-2-2400-4-4004-2-222222-2-22000000-2200000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2-40044004222-2-222222000000-2-200000000000000000000000000000000
χ4944-4-444-400004-4-404-400000004000000-4004-4000000000000000000000000000000000000
χ5044-4-444-400004-4-40-4400000004000000-400-44000000000000000000000000000000000000
χ5144-4-44-4400004-4-4000004i−4i000-4000000400000000004i−4i0000000000000000000000000000
χ5244-4-44-4400004-4-400000−4i4i000-400000040000000000−4i4i0000000000000000000000000000
χ5344-4-4-24-40000-22204-400000−2i32i3-2−2i32i30000200-22−2i32i30000000000000000000000000000000000
χ5444-4-4-24-40000-22204-4000002i3−2i3-22i3−2i30000200-222i3−2i30000000000000000000000000000000000
χ5544-4-4-24-40000-2220-4400000−2i32i3-2−2i32i300002002-22i3−2i30000000000000000000000000000000000
χ5644-4-4-24-40000-2220-44000002i3−2i3-22i3−2i300002002-2−2i32i30000000000000000000000000000000000
χ5744-4-4-2-440000-222000004i−4i0−2i32i322i3−2i30000-20000000023−23−2i2i0000000000000000000000000000
χ5844-4-4-2-440000-222000004i−4i02i3−2i32−2i32i30000-200000000−2323−2i2i0000000000000000000000000000
χ5944-4-4-2-440000-22200000−4i4i0−2i32i322i3−2i30000-200000000−23232i−2i0000000000000000000000000000
χ6044-4-4-2-440000-22200000−4i4i02i3−2i32−2i32i30000-20000000023−232i−2i0000000000000000000000000000
χ614-44-4400004i−4i-44-40000000000000004i−4i000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ624-44-4400004i−4i-44-40000000000000004i−4i00000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ634-44-440000−4i4i-44-4000000000000000−4i4i00000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ644-44-440000−4i4i-44-4000000000000000−4i4i000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ654-4-444004i−4i00-4-4400000000000004i−4i0000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ664-4-444004i−4i00-4-4400000000000004i−4i000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ674-4-44400−4i4i00-4-440000000000000−4i4i0000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ684-4-44400−4i4i00-4-440000000000000−4i4i000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ698-88-8-400008i−8i4-44000000000000000−4i4i00000000000000000000000000000000000000000
χ708-88-8-40000−8i8i4-440000000000000004i−4i00000000000000000000000000000000000000000
χ718-8-88-4008i−8i0044-40000000000000−4i4i0000000000000000000000000000000000000000000
χ728-8-88-400−8i8i0044-400000000000004i−4i0000000000000000000000000000000000000000000

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