Finite Group Databasebeta

← Group #93513

Character table — Group #93513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order1244222444222244448888888824888888888888888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-111-1-1111111-1-1-1-1-1-1-1-111ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ101111111111-1-111-1-1111111-1-1-1-1-1-1-1-111ii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ111111111111-1-111-1-1111111-1-1-1-1-1-1-1-111−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ121111111111-1-111-1-1111111-1-1-1-1-1-1-1-111−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ141111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ151111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ161111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ17222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ18222222222222-2-222-2-2-2-2-2-22222-2-2-2-222000000000000000000000000
χ192222222222-2-222-2-222-2-2-2-22222-2-222-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ2122222-2-22-2-2002-2002-200002i2i−2i−2i002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000000000
χ2222222-2-22-2-2002-2002-200002i2i−2i−2i002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000000000
χ2322222-2-22-2-2002-2002-20000−2i−2i2i2i00−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000000000
χ2422222-2-22-2-2002-2002-20000−2i−2i2i2i00−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000000000
χ2522222-2-22-2-200-2200-2200002i2i−2i−2i00−2i2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000000000000
χ2622222-2-22-2-200-2200-2200002i2i−2i−2i00−2i2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000000000000000
χ2722222-2-22-2-200-2200-220000−2i−2i2i2i002i−2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000000000000000
χ2822222-2-22-2-200-2200-220000−2i−2i2i2i002i−2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000000000000000
χ292222-22-2-22-22-2002-20000002i−2i2i−2i00002i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ302222-22-2-22-22-2002-20000002i−2i2i−2i00002i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ312222-22-2-22-22-2002-2000000−2i2i−2i2i0000−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ322222-22-2-22-22-2002-2000000−2i2i−2i2i0000−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ332222-22-2-22-2-2200-220000002i−2i2i−2i0000−2i2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ342222-22-2-22-2-2200-220000002i−2i2i−2i0000−2i2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ352222-22-2-22-2-2200-22000000−2i2i−2i2i00002i−2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ362222-22-2-22-2-2200-22000000−2i2i−2i2i00002i−2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ3722-2-2222-2-2-22222-2-2-2-200000000-22000000000000000000002−22−22−22−2
χ3822-2-2222-2-2-22222-2-2-2-200000000-2200000000000000000000−22−22−22−22
χ3922-2-2222-2-2-222-2-2-2-222000000002-200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ4022-2-2222-2-2-222-2-2-2-222000000002-200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ4122-2-2222-2-2-2-2-22222-2-2000000002-200000000000000000000i2−i2−i2i2i2−i2−i2i2
χ4222-2-2222-2-2-2-2-22222-2-2000000002-200000000000000000000−i2i2i2−i2−i2i2i2−i2
χ4322-2-2222-2-2-2-2-2-2-2222200000000-22000000000000000000002−2−22−222−2
χ4422-2-2222-2-2-2-2-2-2-2222200000000-2200000000000000000000−222−22−2−22
χ454444-4-44-4-440000000000004-4-44000000000000000000000000000000
χ464444-4-44-4-44000000000000-444-4000000000000000000000000000000
χ4744-4-44-4-4-444004-400-4400000000000000000000000000000000000000
χ4844-4-44-4-4-44400-44004-400000000000000000000000000000000000000
χ4944-4-4-44-44-444-400-440000000000000000000000000000000000000000
χ5044-4-4-44-44-44-44004-40000000000000000000000000000000000000000
χ5144-4-4-4-4444-4000000004i4i−4i−4i0000000000000000000000000000000000
χ5244-4-4-4-4444-400000000−4i−4i4i4i0000000000000000000000000000000000
χ538-88i−8i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000
χ548-88i−8i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000
χ558-8−8i8i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000
χ568-8−8i8i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.