Finite Group Databasebeta

← Group #122104

Character table — Group #122104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444224444444488888888444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1-1-111-1-111ii−i−i−i−iii−i−iii
χ111111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-111−i−iiiii−i−i−i−iii
χ121111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-111-1-11111-1-1−i−iii−i−iiiii−i−i
χ131111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iii−i−iii
χ141111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1-1-111-1-111−i−iiiii−i−iii−i−i
χ151111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i
χ161111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-111-1-11111-1-1ii−i−iii−i−i−i−iii
χ1722222222-2-22222222-2-2-2-2-2-2-200000000000000002-22-2000000000000
χ1822222222-2-22222222-2-2-2-2-2-2-20000000000000000-22-22000000000000
χ1922222222-2-2-2-2-2-2-2-22-2-2-2222200000000000000002-2-22000000000000
χ2022222222-2-2-2-2-2-2-2-22-2-2-222220000000000000000-222-2000000000000
χ21222222-2-2222222-2-2-22-2-22-22-20000000000002-22-20000000000000000
χ22222222-2-2222222-2-2-22-2-22-22-2000000000000-22-220000000000000000
χ23222222-2-222-2-2-2-222-22-2-2-22-220000000000002-2-220000000000000000
χ24222222-2-222-2-2-2-222-22-2-2-22-22000000000000-222-20000000000000000
χ25222222-2-2-2-22222-2-2-2-222-22-22000000002-22-200000000000000000000
χ26222222-2-2-2-22222-2-2-2-222-22-2200000000-22-2200000000000000000000
χ27222222-2-2-2-2-2-2-2-222-2-2222-22-2000000002-2-2200000000000000000000
χ28222222-2-2-2-2-2-2-2-222-2-2222-22-200000000-222-200000000000000000000
χ292222-2-2222222-2-22-2-2-22-2-222-222-2-222-2-2000000000000000000000000
χ302222-2-2222222-2-22-2-2-22-2-222-2-2-222-2-222000000000000000000000000
χ312222-2-22222-2-222-22-2-22-22-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322222-2-22222-2-222-22-2-22-22-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332222-2-222-2-222-2-22-2-22-222-2-2200000000000000000000000000002-22-2
χ342222-2-222-2-222-2-22-2-22-222-2-220000000000000000000000000000-22-22
χ352222-2-222-2-2-2-222-22-22-22-222-200000000000000000000000000002i−2i−2i2i
χ362222-2-222-2-2-2-222-22-22-22-222-20000000000000000000000000000−2i2i2i−2i
χ372222-2-2-2-22222-2-2-222-2-22-2-2220000000000000000000000002i−2i2i−2i0000
χ382222-2-2-2-22222-2-2-222-2-22-2-222000000000000000000000000−2i2i−2i2i0000
χ392222-2-2-2-222-2-2222-22-2-2222-2-20000000000000000000000002-2-220000
χ402222-2-2-2-222-2-2222-22-2-2222-2-2000000000000000000000000-222-20000
χ412222-2-2-2-2-2-222-2-2-22222-222-2-2000000000000000000002-22-200000000
χ422222-2-2-2-2-2-222-2-2-22222-222-2-200000000000000000000-22-2200000000
χ432222-2-2-2-2-2-2-2-2222-2222-2-2-222000000000000000000002i−2i−2i2i00000000
χ442222-2-2-2-2-2-2-2-2222-2222-2-2-22200000000000000000000−2i2i2i−2i00000000
χ4544-4-44-400004i−4i4i−4i00000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ4644-4-44-400004i−4i4i−4i0000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ4744-4-44-40000−4i4i−4i4i00000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ4844-4-44-40000−4i4i−4i4i0000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ4944-4-4-4400004i−4i−4i4i00000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ5044-4-4-4400004i−4i−4i4i0000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ5144-4-4-440000−4i4i4i−4i00000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ5244-4-4-440000−4i4i4i−4i0000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ538-88-800008i−8i0000000000000000000000000000000000000000000000
χ548-88-80000−8i8i0000000000000000000000000000000000000000000000
χ558-8-88008i−8i000000000000000000000000000000000000000000000000
χ568-8-8800−8i8i000000000000000000000000000000000000000000000000

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