Finite Group Databasebeta

← Group #10692818

Character table — Group #10692818

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212161616161616161616161616242424242424242424244848
order122222344446664444444466121212121212121244121212121212121212124444246688121224242424444444888888
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
χ511111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ711111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1
χ811111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ91111-1-11-1-1-1-1111-111ii−i−i1-1-111-1-1-1-1-1-1i−i11iiii−i−i−i−iii−i−i1-111i−i-1-1ii−i−i11-1-1i−i11-1-1i−i
χ101111-1-11-1-1-1-1111-111ii−i−i1-1-111-1-1-1-1-1-1i−i11iiii−i−i−i−iii−i−i-11-1-1−ii11−i−iii11-1-1i−i-1-111−ii
χ111111-1-11-1-1-1-1111-111ii−i−i1-1-111-1-1-1-1-1-1i−i11iiii−i−i−i−i−i−iii1-111i−i-1-1ii−i−i-1-111−ii-1-111−ii
χ121111-1-11-1-1-1-1111-111ii−i−i1-1-111-1-1-1-1-1-1i−i11iiii−i−i−i−i−i−iii-11-1-1−ii11−i−iii-1-111−ii11-1-1i−i
χ131111-1-11-1-1-1-1111-111−i−iii1-1-111-1-1-1-1-1-1−ii11−i−i−i−iiiiiii−i−i1-111−ii-1-1−i−iii-1-111i−i-1-111i−i
χ141111-1-11-1-1-1-1111-111−i−iii1-1-111-1-1-1-1-1-1−ii11−i−i−i−iiiiiii−i−i-11-1-1i−i11ii−i−i-1-111i−i11-1-1−ii
χ151111-1-11-1-1-1-1111-111−i−iii1-1-111-1-1-1-1-1-1−ii11−i−i−i−iiiii−i−iii1-111−ii-1-1−i−iii11-1-1−ii11-1-1−ii
χ161111-1-11-1-1-1-1111-111−i−iii1-1-111-1-1-1-1-1-1−ii11−i−i−i−iiiii−i−iii-11-1-1i−i11ii−i−i11-1-1−ii-1-111i−i
χ17222222222-2-2222-22-22222-222-2-2-2-2-2-222-2-22-222-2-222-2-20000000000000000000000000000
χ18222222222-2-2222-22-2-2-2-2-2-222-2-2-2-2-2-222222-2-2-222-2-2220000000000000000000000000000
χ192222222-2-222222-2-220000-2222222-2-2-2-200-2-20000000022220000000000000000-2-2000000
χ202222222-2-222222-2-220000-2222222-2-2-2-200-2-200000000-2-2-2-2000000000000000022000000
χ212222222-2-2-2-22222-2-20000222-2-2-2-222-2-200-220000000000000000000000002-22-200000000
χ222222222-2-2-2-22222-2-20000222-2-2-2-222-2-200-22000000000000000000000000-22-2200000000
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
χ25222222-12222-1-1-1222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-2-2-1-111111111000022-1-1-2-2-1-11111000000000000
χ26222222-12222-1-1-1222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2112211-1-1-1-1000000000000
χ27222222-122-2-2-1-1-1-22-22222-2-1-1111111-1-1-2-2-11-1-111-1-111000000−i3i300−i3i3−i3i3−i3i3000000000000
χ28222222-122-2-2-1-1-1-22-22222-2-1-1111111-1-1-2-2-11-1-111-1-111000000i3−i300i3−i3i3−i3i3−i3000000000000
χ29222222-122-2-2-1-1-1-22-2-2-2-2-2-2-1-1111111-1-122-1111-1-111-1-1000000−i3i300−i3i3i3−i3i3−i3000000000000
χ30222222-122-2-2-1-1-1-22-2-2-2-2-2-2-1-1111111-1-122-1111-1-111-1-1000000i3−i300i3−i3−i3i3−i3i3000000000000
χ312222-2-222222222-2-2-200002-2-2-2-222-2-22200-220000000000000000000000002-2-2200000000
χ322222-2-222222222-2-2-200002-2-2-2-222-2-22200-22000000000000000000000000-222-200000000
χ332222-2-2222-2-22222-220000-2-2-222-2-2222200-2-2000000002i2i−2i−2i0000000000000000−2i2i000000
χ342222-2-2222-2-22222-220000-2-2-222-2-2222200-2-200000000−2i−2i2i2i00000000000000002i−2i000000
χ352222-2-22-2-22222222-22i2i−2i−2i-2-2-2-2-22222-2-2−2i2i2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ362222-2-22-2-22222222-2−2i−2i2i2i-2-2-2-2-22222-2-22i−2i2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ372222-2-2-1-2-222-1-1-122-22i2i−2i−2i-21111-1-1-1-111−2i2i-11−i−iiiii−i−i000000−i3i300i3−i33−3−33000000000000
χ382222-2-2-1-2-222-1-1-122-22i2i−2i−2i-21111-1-1-1-111−2i2i-11−i−iiiii−i−i000000i3−i300−i3i3−333−3000000000000
χ392222-2-2-1-2-222-1-1-122-2−2i−2i2i2i-21111-1-1-1-1112i−2i-11ii−i−i−i−iii000000−i3i300i3−i3−333−3000000000000
χ402222-2-2-1-2-222-1-1-122-2−2i−2i2i2i-21111-1-1-1-1112i−2i-11ii−i−i−i−iii000000i3−i300−i3i33−3−33000000000000
χ412222-2-2-1-2-2-2-2-1-1-1-2222i2i−2i−2i211-1-11111112i−2i-1-1−i−i−i−iiiii00002-2-1-12i−2i11−i−iii000000000000
χ422222-2-2-1-2-2-2-2-1-1-1-2222i2i−2i−2i211-1-11111112i−2i-1-1−i−i−i−iiiii0000-2211−2i2i-1-1ii−i−i000000000000
χ432222-2-2-1-2-2-2-2-1-1-1-222−2i−2i2i2i211-1-1111111−2i2i-1-1iiii−i−i−i−i00002-2-1-1−2i2i11ii−i−i000000000000
χ442222-2-2-1-2-2-2-2-1-1-1-222−2i−2i2i2i211-1-1111111−2i2i-1-1iiii−i−i−i−i0000-22112i−2i-1-1−i−iii000000000000
χ45444444-2-4-444-2-2-2-4-440000-4-2-2-2-2-2-222220022000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-24-4-400004-2-22222-2-222002-2000000000000000000000000000000000000
χ474444-4-4-24444-2-2-2-4-4-4000042222-2-222-2-2002-2000000000000000000000000000000000000
χ484444-4-4-244-4-4-2-2-24-440000-422-2-222-2-2-2-20022000000000000000000000000000000000000
χ4944-4-44-440000-4-44000000004-40000000000000000000000000000000000000000002i−2i2i−2i00
χ5044-4-44-440000-4-44000000004-4000000000000000000000000000000000000000000−2i2i−2i2i00
χ5144-4-4-4440000-4-4400000000-440000000000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-4-4440000-4-4400000000-44000000000000000000000000000000000000000000−2i2i2i−2i00
χ534-44-4004004i−4i4-4-40000000000004i−4i00000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ544-44-4004004i−4i4-4-40000000000004i−4i0000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ554-44-400400−4i4i4-4-4000000000000−4i4i00000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ564-44-400400−4i4i4-4-4000000000000−4i4i0000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ574-4-440044i−4i00-44-40002+2i−2−2i2−2i−2+2i0000000004i−4i00002+2i−2−2i002−2i−2+2i000000000000000000000000000000
χ584-4-440044i−4i00-44-4000−2−2i2+2i−2+2i2−2i0000000004i−4i0000−2−2i2+2i00−2+2i2−2i000000000000000000000000000000
χ594-4-44004−4i4i00-44-40002−2i−2+2i2+2i−2−2i000000000−4i4i00002−2i−2+2i002+2i−2−2i000000000000000000000000000000
χ604-4-44004−4i4i00-44-4000−2+2i2−2i−2−2i2+2i000000000−4i4i0000−2+2i2−2i00−2−2i2+2i000000000000000000000000000000
χ614-4-4400-24i−4i002-220002+2i−2−2i2−2i−2+2i000−2i32i30023−23−2i2i0000−1−i1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−1+i1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000000000
χ624-4-4400-24i−4i002-220002+2i−2−2i2−2i−2+2i0002i3−2i300−2323−2i2i0000−1−i1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−1+i1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000000000
χ634-4-4400-24i−4i002-22000−2−2i2+2i−2+2i2−2i000−2i32i30023−23−2i2i00001+i−1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ111−i−1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000000000
χ644-4-4400-24i−4i002-22000−2−2i2+2i−2+2i2−2i0002i3−2i300−2323−2i2i00001+i−1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ111−i−1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000000000
χ654-4-4400-2−4i4i002-220002−2i−2+2i2+2i−2−2i000−2i32i300−23232i−2i0000−1+i1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−1−i1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000000000
χ664-4-4400-2−4i4i002-220002−2i−2+2i2+2i−2−2i0002i3−2i30023−232i−2i0000−1+i1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−1−i1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000000000
χ674-4-4400-2−4i4i002-22000−2+2i2−2i−2−2i2+2i000−2i32i300−23232i−2i00001−i−1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ111+i−1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000000000
χ684-4-4400-2−4i4i002-22000−2+2i2−2i−2−2i2+2i0002i3−2i30023−232i−2i00001−i−1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ111+i−1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000000000
χ6988-8-88-8-4000044-400000000-44000000000000000000000000000000000000000000000000
χ7088-8-8-88-4000044-4000000004-4000000000000000000000000000000000000000000000000
χ718-88-800-4008i−8i-444000000000000−4i4i00000000000000000000000000000000000000000000
χ728-88-800-400−8i8i-4440000000000004i−4i00000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.