Finite Group Databasebeta

← Group #10692385

Character table — Group #10692385

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212161616161616161616161616242424242424242424244848
order122222344446662244444466661212121212124461212121212121212124444246688121224242424444444444488
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
χ5111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ6111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ7111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1
χ8111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111
χ91111-1-1111-1-11111-11-111-1-111-1-111-1-1111-1-1-111-1-111-1-1ii−i−i1-1111-1-1-111-1-1i−iii−i−iii−i−ii−i
χ101111-1-1111-1-11111-11-111-1-111-1-111-1-1111-1-1-111-1-111-1-1ii−i−i-11-1-1-1111-1-111i−iii−i−i−i−iii−ii
χ111111-1-1111-1-11111-11-111-1-111-1-111-1-1111-1-1-111-1-111-1-1−i−iii1-1111-1-1-111-1-1−ii−i−iii−i−iii−ii
χ121111-1-1111-1-11111-11-111-1-111-1-111-1-1111-1-1-111-1-111-1-1−i−iii-11-1-1-1111-1-111−ii−i−iiiii−i−ii−i
χ131111-1-1111-1-11111-11-1-1-11111-1-111-1-111-11-1-1-1-111-1-111ii−i−i1-111-11-1-1-1-111i−i−i−iii−i−iiii−i
χ141111-1-1111-1-11111-11-1-1-11111-1-111-1-111-11-1-1-1-111-1-111ii−i−i-11-1-11-11111-1-1i−i−i−iiiii−i−i−ii
χ151111-1-1111-1-11111-11-1-1-11111-1-111-1-111-11-1-1-1-111-1-111−i−iii1-111-11-1-1-1-111−iiii−i−iii−i−i−ii
χ161111-1-1111-1-11111-11-1-1-11111-1-111-1-111-11-1-1-1-111-1-111−i−iii-11-1-11-11111-1-1−iiii−i−i−i−iiii−i
χ17222222222-2-2222-2-2-222222-2-222-2-2-2-222-2-2-22-2-2-2-222220000000000000000000000000000
χ18222222222-2-2222-2-2-22-2-2-2-2-2-222-2-2-2-22222-222222-2-2-2-20000000000000000000000000000
χ192222222-2-222222-2-22-20000-2-2222222-2-200-2-2000000002222000000000000-2-20000000000
χ202222222-2-222222-2-22-20000-2-2222222-2-200-2-200000000-2-2-2-2000000000000220000000000
χ212222222-2-2-2-222222-2-200002222-2-2-2-2-2-2002-2000000000000000000000000002-22-2000000
χ222222222-2-2-2-222222-2-200002222-2-2-2-2-2-2002-200000000000000000000000000-22-22000000
χ23222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000022-1-122-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-211-2-2111111000000000000
χ25222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-111111111000022-1-1-2-2-1-11111000000000000
χ26222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2112211-1-1-1-1000000000000
χ27222222-122-2-2-1-1-1-2-2-22222211-1-11111-1-1-2-21-11111-1-1-1-1000000−i3i300−i3i3−i3i3−i3i3000000000000
χ28222222-122-2-2-1-1-1-2-2-22222211-1-11111-1-1-2-21-11111-1-1-1-1000000i3−i300i3−i3i3−i3i3−i3000000000000
χ29222222-122-2-2-1-1-1-2-2-22-2-2-2-211-1-11111-1-1221-1-1-1-1-11111000000−i3i300−i3i3i3−i3i3−i3000000000000
χ30222222-122-2-2-1-1-1-2-2-22-2-2-2-211-1-11111-1-1221-1-1-1-1-11111000000i3−i300i3−i3−i3i3−i3i3000000000000
χ312222-2-222222222-22-2-222-2-2-2-2-2-2-2-22222-222-2-2-22222-2-20000000000000000000000000000
χ322222-2-222222222-22-2-2-2-222-2-2-2-2-2-222222-22-222-2-2-2-2220000000000000000000000000000
χ332222-2-22-2-2222222-2-22000022-2-2-2-222-2-200-22000000000000000000000000002i−2i−2i2i000000
χ342222-2-22-2-2222222-2-22000022-2-2-2-222-2-200-2200000000000000000000000000−2i2i2i−2i000000
χ352222-2-22-2-2-2-2222-22220000-2-2-2-222-2-2-2-20022000000002i2i−2i−2i000000000000−2i2i0000000000
χ362222-2-22-2-2-2-2222-22220000-2-2-2-222-2-2-2-2002200000000−2i−2i2i2i0000000000002i−2i0000000000
χ372222-2-2-12222-1-1-1-22-2-222-2-2111111-1-1-1-1-22-1111-1-1-1-111000000−i3i300i3−i3−i3i3i3−i3000000000000
χ382222-2-2-12222-1-1-1-22-2-222-2-2111111-1-1-1-1-22-1111-1-1-1-111000000i3−i300−i3i3i3−i3−i3i3000000000000
χ392222-2-2-12222-1-1-1-22-2-2-2-222111111-1-1-1-12-2-11-1-11111-1-1000000−i3i300i3−i3i3−i3−i3i3000000000000
χ402222-2-2-12222-1-1-1-22-2-2-2-222111111-1-1-1-12-2-11-1-11111-1-1000000i3−i300−i3i3−i3i3i3−i3000000000000
χ412222-2-2-122-2-2-1-1-12-22-222-2-2-1-111-1-111-1-12-211-1-111-1-11100002-2-1-12-211-1-111000000000000
χ422222-2-2-122-2-2-1-1-12-22-222-2-2-1-111-1-111-1-12-211-1-111-1-1110000-2211-22-1-111-1-1000000000000
χ432222-2-2-122-2-2-1-1-12-22-2-2-222-1-111-1-111-1-1-221111-1-111-1-100002-2-1-1-221111-1-1000000000000
χ442222-2-2-122-2-2-1-1-12-22-2-2-222-1-111-1-111-1-1-221111-1-111-1-10000-22112-2-1-1-1-111000000000000
χ45444444-2-4-444-2-2-2-4-44-4000022-2-2-2-2-2-2220022000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-244-4-40000-2-2-2-222222200-22000000000000000000000000000000000000
χ474444-4-4-2-4-444-2-2-24-4-440000-2-22222-2-222002-2000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-2-444400002222-2-2222200-2-2000000000000000000000000000000000000
χ4944-4-4004004i−4i4-4-4000000000000004i−4i000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ5044-4-4004004i−4i4-4-4000000000000004i−4i00000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ5144-4-400400−4i4i4-4-400000000000000−4i4i000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ5244-4-400400−4i4i4-4-400000000000000−4i4i00000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ534-44-40044-400-44-40000004i−4i000000004-400000000004i−4i0000000000000000000000000000
χ544-44-40044-400-44-4000000−4i4i000000004-40000000000−4i4i0000000000000000000000000000
χ554-44-4004-4400-44-400004i−4i0000000000-44000000004i−4i000000000000000000000000000000
χ564-44-4004-4400-44-40000−4i4i0000000000-4400000000−4i4i000000000000000000000000000000
χ574-44-400-24-4002-220000004i−4i−2i32i300−2i32i300-2200000023−2300−2i2i0000000000000000000000000000
χ584-44-400-24-4002-220000004i−4i2i3−2i3002i3−2i300-22000000−232300−2i2i0000000000000000000000000000
χ594-44-400-24-4002-22000000−4i4i−2i32i300−2i32i300-22000000−2323002i−2i0000000000000000000000000000
χ604-44-400-24-4002-22000000−4i4i2i3−2i3002i3−2i300-2200000023−23002i−2i0000000000000000000000000000
χ614-44-400-2-44002-2200004i−4i00−2i32i3002i3−2i3002-2000023−2300−2i2i000000000000000000000000000000
χ624-44-400-2-44002-2200004i−4i002i3−2i300−2i32i3002-20000−232300−2i2i000000000000000000000000000000
χ634-44-400-2-44002-220000−4i4i00−2i32i3002i3−2i3002-20000−2323002i−2i000000000000000000000000000000
χ644-44-400-2-44002-220000−4i4i002i3−2i300−2i32i3002-2000023−23002i−2i000000000000000000000000000000
χ654-4-444-440000-4-4400000000004-400000000000000000000000000000000000000002i−2i2i−2i00
χ664-4-444-440000-4-4400000000004-40000000000000000000000000000000000000000−2i2i−2i2i00
χ674-4-44-4440000-4-440000000000-4400000000000000000000000000000000000000002-2-2200
χ684-4-44-4440000-4-440000000000-440000000000000000000000000000000000000000-222-200
χ6988-8-800-4008i−8i-44400000000000000−4i4i000000000000000000000000000000000000000000
χ7088-8-800-400−8i8i-444000000000000004i−4i000000000000000000000000000000000000000000
χ718-8-888-8-4000044-40000000000-440000000000000000000000000000000000000000000000
χ728-8-88-88-4000044-400000000004-40000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).