Finite Group Databasebeta

← Group #10692371

Character table — Group #10692371

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212161616161616161616161616242424242424242424244848
order1222223444466622444444666612121212121222666661212121212444444881212121224242424444444444488
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
χ5111111111111111111-1-1-1-11111111111-1-11-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ6111111111111111111-1-1-1-11111111111-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ7111111111111111111-1-1-1-11111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1
χ8111111111111111111-1-1-1-11111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111
χ91111-1-1111-1-11111-11-111-1-111-1-111-1-1111-1-111-1-1-111-1-1ii−i−i1-11-111-1-111-1-1i−iii−i−iii−i−ii−i
χ101111-1-1111-1-11111-11-111-1-111-1-111-1-1111-1-111-1-1-111-1-1ii−i−i-11-11-1-111-1-111i−iii−i−i−i−iii−ii
χ111111-1-1111-1-11111-11-111-1-111-1-111-1-1111-1-111-1-1-111-1-1−i−iii1-11-111-1-111-1-1−ii−i−iii−i−iii−ii
χ121111-1-1111-1-11111-11-111-1-111-1-111-1-1111-1-111-1-1-111-1-1−i−iii-11-11-1-111-1-111−ii−i−iiiii−i−ii−i
χ131111-1-1111-1-11111-11-1-1-11111-1-111-1-111-11-1-1-111-1-1-111ii−i−i1-1-1111-1-1-1-111i−i−i−iii−i−iiii−i
χ141111-1-1111-1-11111-11-1-1-11111-1-111-1-111-11-1-1-111-1-1-111ii−i−i-111-1-1-11111-1-1i−i−i−iiiii−i−i−ii
χ151111-1-1111-1-11111-11-1-1-11111-1-111-1-111-11-1-1-111-1-1-111−i−iii1-1-1111-1-1-1-111−iiii−i−iii−i−i−ii
χ161111-1-1111-1-11111-11-1-1-11111-1-111-1-111-11-1-1-111-1-1-111−i−iii-111-1-1-11111-1-1−iiii−i−i−i−iiii−i
χ17222222222-2-2222-2-2-222222-2-222-2-2-2-222-2-2-2-2-2-2-2222220000000000000000000000000000
χ18222222222-2-2222-2-2-22-2-2-2-2-2-222-2-2-2-22222-222222-2-2-2-20000000000000000000000000000
χ192222222-2-222222-2-22-20000-2-2222222-2-200-20000-200002222000000000000-2-20000000000
χ202222222-2-222222-2-22-20000-2-2222222-2-200-20000-20000-2-2-2-2000000000000220000000000
χ212222222-2-2-2-222222-2-200002222-2-2-2-2-2-20020000-200000000000000000000002-22-2000000
χ222222222-2-2-2-222222-2-200002222-2-2-2-2-2-20020000-20000000000000000000000-22-22000000
χ23222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-211111111000000000000
χ25222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-11111-11111000022-2-2-1-1-1-11111000000000000
χ26222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-11111-111110000-2-2221111-1-1-1-1000000000000
χ27222222-122-2-2-1-1-1-2-2-22222211-1-11111-1-1-2-211111-1-1-1-1-100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-122-2-2-1-1-1-2-2-22222211-1-11111-1-1-2-211111-1-1-1-1-100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-122-2-2-1-1-1-2-2-22-2-2-2-211-1-11111-1-1221-1-1-1-1-1111100000000−i3i3−i3i3i3−i3i3−i3000000000000
χ30222222-122-2-2-1-1-1-2-2-22-2-2-2-211-1-11111-1-1221-1-1-1-1-1111100000000i3−i3i3−i3−i3i3−i3i3000000000000
χ312222-2-222222222-22-2-222-2-2-2-2-2-2-2-22222-222-2-222-222-2-20000000000000000000000000000
χ322222-2-222222222-22-2-2-2-222-2-2-2-2-2-222222-2222-2-2-2-2-2220000000000000000000000000000
χ332222-2-22-2-2222222-2-22000022-2-2-2-222-2-200-20000200000000000000000000002i−2i−2i2i000000
χ342222-2-22-2-2222222-2-22000022-2-2-2-222-2-200-2000020000000000000000000000−2i2i2i−2i000000
χ352222-2-22-2-2-2-2222-22220000-2-2-2-222-2-2-2-20020000200002i2i−2i−2i000000000000−2i2i0000000000
χ362222-2-22-2-2-2-2222-22220000-2-2-2-222-2-2-2-2002000020000−2i−2i2i2i0000000000002i−2i0000000000
χ372222-2-2-12222-1-1-1-22-2-222-2-2111111-1-1-1-1-22-111-1-11-1-11100000000−i3i3i3−i3−i3i3i3−i3000000000000
χ382222-2-2-12222-1-1-1-22-2-222-2-2111111-1-1-1-1-22-111-1-11-1-11100000000i3−i3−i3i3i3−i3−i3i3000000000000
χ392222-2-2-12222-1-1-1-22-2-2-2-222111111-1-1-1-12-2-1-1-111111-1-100000000−i3i3i3−i3i3−i3−i3i3000000000000
χ402222-2-2-12222-1-1-1-22-2-2-2-222111111-1-1-1-12-2-1-1-111111-1-100000000i3−i3−i3i3−i3i3i3−i3000000000000
χ412222-2-2-122-2-2-1-1-12-22-222-2-2-1-111-1-111-1-12-21-1-1111-1-11100002-22-2-1-111-1-111000000000000
χ422222-2-2-122-2-2-1-1-12-22-222-2-2-1-111-1-111-1-12-21-1-1111-1-1110000-22-2211-1-111-1-1000000000000
χ432222-2-2-122-2-2-1-1-12-22-2-2-222-1-111-1-111-1-1-22111-1-1111-1-100002-2-22-1-11111-1-1000000000000
χ442222-2-2-122-2-2-1-1-12-22-2-2-222-1-111-1-111-1-1-22111-1-1111-1-10000-222-211-1-1-1-111000000000000
χ45444444-2-4-444-2-2-2-4-44-4000022-2-2-2-2-2-2220020000200000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-244-4-40000-2-2-2-222222200-20000200000000000000000000000000000000
χ474444-4-4-2-4-444-2-2-24-4-440000-2-22222-2-2220020000-200000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-2-444400002222-2-2222200-20000-200000000000000000000000000000000
χ4944-4-44-4400004-4-400000000004-400000000000000000000000000000000000000002-22-200
χ5044-4-44-4400004-4-400000000004-40000000000000000000000000000000000000000-22-2200
χ5144-4-4-44400004-4-40000000000-4400000000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-4-44400004-4-40000000000-440000000000000000000000000000000000000000−2i2i2i−2i00
χ534-44-4004004i−4i-44-4000000000000004i−4i000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ544-44-4004004i−4i-44-4000000000000004i−4i00000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ554-44-400400−4i4i-44-400000000000000−4i4i000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ564-44-400400−4i4i-44-400000000000000−4i4i00000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ574-4-440044-400-4-440000004-4000000004-400000000004-40000000000000000000000000000
χ584-4-440044-400-4-44000000-44000000004-40000000000-440000000000000000000000000000
χ594-4-44004-4400-4-4400004-40000000000-44000000004-4000000000000000000000000000000
χ604-4-44004-4400-4-440000-440000000000-4400000000-44000000000000000000000000000000
χ614-4-4400-24-40022-20000004-4−2i32i300−2i32i300-2200000−2i32i3000-220000000000000000000000000000
χ624-4-4400-24-40022-20000004-42i3−2i3002i3−2i300-22000002i3−2i3000-220000000000000000000000000000
χ634-4-4400-24-40022-2000000-44−2i32i300−2i32i300-22000002i3−2i30002-20000000000000000000000000000
χ644-4-4400-24-40022-2000000-442i3−2i3002i3−2i300-2200000−2i32i30002-20000000000000000000000000000
χ654-4-4400-2-440022-200004-400−2i32i3002i3−2i3002-2000−2i32i3000-22000000000000000000000000000000
χ664-4-4400-2-440022-200004-4002i3−2i300−2i32i3002-20002i3−2i3000-22000000000000000000000000000000
χ674-4-4400-2-440022-20000-4400−2i32i3002i3−2i3002-20002i3−2i30002-2000000000000000000000000000000
χ684-4-4400-2-440022-20000-44002i3−2i300−2i32i3002-2000−2i32i30002-2000000000000000000000000000000
χ6988-8-88-8-40000-4440000000000-440000000000000000000000000000000000000000000000
χ7088-8-8-88-40000-44400000000004-40000000000000000000000000000000000000000000000
χ718-88-800-4008i−8i4-4400000000000000−4i4i000000000000000000000000000000000000000000
χ728-88-800-400−8i8i4-44000000000000004i−4i000000000000000000000000000000000000000000

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