Finite Group Databasebeta

← Group #112043

Character table — Group #112043

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444224444444488888888222444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1
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
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-111-1-1-1-1-1-11111-11-1-1iiii−i−i−i−i111-1-1-1-1111-1-1ii−i−iii−i−iii−i−i
χ10111111-1-111-1-1-1-1-1-11111-11-1-1iiii−i−i−i−i11-111-1-1-1-1-111−i−iiiii−i−i−i−iii
χ11111111-1-111-1-1-1-1-1-11111-11-1-1iiii−i−i−i−i-1-11-1-1111-1-111ii−i−i−i−iii−i−iii
χ12111111-1-111-1-1-1-1-1-11111-11-1-1iiii−i−i−i−i-1-1-11111-111-1-1−i−iii−i−iiiii−i−i
χ13111111-1-111-1-1-1-1-1-11111-11-1-1−i−i−i−iiiii111-1-1-1-1111-1-1−i−iii−i−iii−i−iii
χ14111111-1-111-1-1-1-1-1-11111-11-1-1−i−i−i−iiiii11-111-1-1-1-1-111ii−i−i−i−iiiii−i−i
χ15111111-1-111-1-1-1-1-1-11111-11-1-1−i−i−i−iiiii-1-11-1-1111-1-111−i−iiiii−i−iii−i−i
χ16111111-1-111-1-1-1-1-1-11111-11-1-1−i−i−i−iiiii-1-1-11111-111-1-1ii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-2-2-2-2-222-22000000000022-200-20000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-220000000000-2-220020000000000000000
χ1922222222-2-22222-2-222-2-2-2-22-2000000002-20002-200000000000000000
χ2022222222-2-22222-2-222-2-2-2-22-200000000-22000-2200000000000000000
χ2122222222-2-222-2-222-2-222-2-2-2-200000000000000002-22-2000000000000
χ2222222222-2-222-2-222-2-222-2-2-2-20000000000000000-22-22000000000000
χ23222222-2-222-2-22222-2-2-2-2-222-200000000002-2200-20000000000000000
χ24222222-2-222-2-22222-2-2-2-2-222-20000000000-22-20020000000000000000
χ25222222-2-2-2-2-2-222-2-2-2-2222-22200000000000000002-2-22000000000000
χ26222222-2-2-2-2-2-222-2-2-2-2222-2220000000000000000-222-2000000000000
χ27222222-2-2-2-2-2-2-2-22222-2-22-2-22000000002-2000-2200000000000000000
χ28222222-2-2-2-2-2-2-2-22222-2-22-2-2200000000-220002-200000000000000000
χ292222-2-22222-2-2222-22-22-22-2-2-200000000000000000000000000002i−2i2i−2i
χ302222-2-22222-2-2222-22-22-22-2-2-20000000000000000000000000000−2i2i−2i2i
χ312222-2-22222-2-2-2-2-22-22-222-22-20000000000000000000000002i−2i2i−2i0000
χ322222-2-22222-2-2-2-2-22-22-222-22-2000000000000000000000000−2i2i−2i2i0000
χ332222-2-222-2-2-2-222-222-2-22-22-22000000000000000000002-22-200000000
χ342222-2-222-2-2-2-222-222-2-22-22-2200000000000000000000-22-2200000000
χ352222-2-222-2-2-2-2-2-22-2-222-2-22222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ362222-2-222-2-2-2-2-2-22-2-222-2-2222−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ372222-2-2-2-22222222-2-22-22-2-2-220000000000000000000000002-2-220000
χ382222-2-2-2-22222222-2-22-22-2-2-22000000000000000000000000-222-20000
χ392222-2-2-2-22222-2-2-222-22-2-2-22200000000000000000000000000002-2-22
χ402222-2-2-2-22222-2-2-222-22-2-2-2220000000000000000000000000000-222-2
χ412222-2-2-2-2-2-22222-22-222-222-2-222-2-2-2-222000000000000000000000000
χ422222-2-2-2-2-2-22222-22-222-222-2-2-2-22222-2-2000000000000000000000000
χ432222-2-2-2-2-2-222-2-22-22-2-22222-2000000000000000000002i−2i−2i2i00000000
χ442222-2-2-2-2-2-222-2-22-22-2-22222-200000000000000000000−2i2i2i−2i00000000
χ4544-4-44-44i−4i004i−4i0000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ4644-4-44-44i−4i004i−4i000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ4744-4-44-4−4i4i00−4i4i0000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ4844-4-44-4−4i4i00−4i4i000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ4944-4-4-444i−4i00−4i4i0000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ5044-4-4-444i−4i00−4i4i000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ5144-4-4-44−4i4i004i−4i0000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ5244-4-4-44−4i4i004i−4i000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ538-88-8000000008i−8i000000000000000000000000000000000000000000
χ548-88-800000000−8i8i000000000000000000000000000000000000000000
χ558-8-8800008-80000000000000000000000000000000000000000000000
χ568-8-880000-880000000000000000000000000000000000000000000000

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