Finite Group Databasebeta

← Group #129727

Character table — Group #129727

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order1244222444222244448888888824888822444444444444441616161616161616
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
χ5111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-111-1-111-1-1-1-11111-1-111-1-11-11-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-111-1-111-1-1-1-11111-1-111-1-11-11-111-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-11-11-1-11111-1-111-1-1-1-111-1-111
χ121111111111-1-111-1-111-1-1-1-11111-1-111-1-1-11-11-1-111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ18222222222222-2-222-2-222222222-2-2-2-2-2-2000000000000000000000000
χ192222222222-2-222-2-2222222-2-2-2-2-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222000000000000000000000000
χ2122-2-2222-2-2-22222-2-2-2-200000000-22000000000000000000002−22−22−22−2
χ2222-2-2222-2-2-22222-2-2-2-200000000-2200000000000000000000−22−22−22−22
χ2322-2-2222-2-2-222-2-2-2-222000000002-200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ2422-2-2222-2-2-222-2-2-2-222000000002-200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ2522-2-2222-2-2-2-2-22222-2-2000000002-2000000000000000000002−2−222−2−22
χ2622-2-2222-2-2-2-2-22222-2-2000000002-200000000000000000000−222−2−222−2
χ2722-2-2222-2-2-2-2-2-2-2222200000000-2200000000000000000000i2−i2−i2i2−i2i2i2−i2
χ2822-2-2222-2-2-2-2-2-2-2222200000000-2200000000000000000000−i2i2i2−i2i2−i2−i2i2
χ2922-2-22-2-222-22-2002-2002i2i−2i−2i2i2i−2i−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ3022-2-22-2-222-22-2002-2002i2i−2i−2i2i2i−2i−2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ3122-2-22-2-222-22-2002-200−2i−2i2i2i−2i−2i2i2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ3222-2-22-2-222-22-2002-200−2i−2i2i2i−2i−2i2i2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ3322-2-22-2-222-2-2200-22002i2i−2i−2i−2i−2i2i2i000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ3422-2-22-2-222-2-2200-22002i2i−2i−2i−2i−2i2i2i00000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ3522-2-22-2-222-2-2200-2200−2i−2i2i2i2i2i−2i−2i000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ3622-2-22-2-222-2-2200-2200−2i−2i2i2i2i2i−2i−2i00000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ3722-2-2-2-222-22002-2002-200002-22-2002-200020-2002-20000000000000000
χ3822-2-2-2-222-22002-2002-200002-22-2002-2000-20200-220000000000000000
χ3922-2-2-2-222-22002-2002-20000-22-2200-220020-202-2000000000000000000
χ4022-2-2-2-222-22002-2002-20000-22-2200-2200-2020-22000000000000000000
χ4122-2-2-2-222-2200-2200-2200002-22-200-220020-20-22000000000000000000
χ4222-2-2-2-222-2200-2200-2200002-22-200-2200-20202-2000000000000000000
χ4322-2-2-2-222-2200-2200-220000-22-22002-200020-200-220000000000000000
χ4422-2-2-2-222-2200-2200-220000-22-22002-2000-202002-20000000000000000
χ4544444-4-4-4-444-400-440000000000000000000000000000000000000000
χ4644444-4-4-4-44-44004-40000000000000000000000000000000000000000
χ474444-44-44-4-40000000000004i−4i−4i4i000000000000000000000000000000
χ484444-44-44-4-4000000000000−4i4i4i−4i000000000000000000000000000000
χ494444-4-44-44-4004-400-4400000000000000000000000000000000000000
χ504444-4-44-44-400-44004-400000000000000000000000000000000000000
χ5144-4-4-44-4-444000000000000000000004-4000000000000000000000000
χ5244-4-4-44-4-44400000000000000000000-44000000000000000000000000
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.