Finite Group Databasebeta

← Group #243137

Character table — Group #243137

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12224444444444222444444488888888224488888888888888888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111-1-1-1-1-1-111111-1-11-1-1-11111111-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-1-1-111111-1-11-1-1-11111111-1-1-1-11-11-1-1-111-1-11111-1-1-1-111-1-111
χ111111-1-1-1-1-1-111111-1-11-1-1-11111111-1-1-1-1-11-1111-1-1-1-111-1-11111-1-1-1-111
χ121111-1-1-1-1-1-111111-1-11-1-1-11111111-1-1-1-1-11-11-1-11111-1-1-1-111-1-11111-1-1
χ131111-1-1-1-1-1-111111-1-11-1-1-1111-1-1-1-111111-11-111-1-1-1-111-1-111-1-11111-1-1
χ141111-1-1-1-1-1-111111-1-11-1-1-1111-1-1-1-111111-11-1-1-11111-1-1-1-11111-1-1-1-111
χ151111-1-1-1-1-1-111111-1-11-1-1-1111-1-1-1-11111-11-1111-1-111-1-111-1-1-1-111-1-111
χ161111-1-1-1-1-1-111111-1-11-1-1-1111-1-1-1-11111-11-11-1-111-1-11111-1-111-1-111-1-1
χ172222222222-222-2-22-22-2-2-22-2-20000000000000000000000002i−2i2i−2i0000
χ182222222222-222-2-22-22-2-2-22-2-2000000000000000000000000−2i2i−2i2i0000
χ1922222222-2-22222-2-22-2-2-22-22-200000000000000000000000000002-22-2
χ2022222222-2-22222-2-22-2-2-22-22-20000000000000000000000000000-22-22
χ2122222222-2-2-222-22-2-2-222-2-2-22000000000000000000002i−2i2i−2i00000000
χ2222222222-2-2-222-22-2-2-222-2-2-2200000000000000000000−2i2i−2i2i00000000
χ23222222-2-2222-2-222-2-222-22-2-2-20000000000002i−2i2i−2i0000000000000000
χ24222222-2-2222-2-222-2-222-22-2-2-2000000000000−2i2i−2i2i0000000000000000
χ25222222-2-222-2-2-2-2-2-222-22-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ26222222-2-222-2-2-2-2-2-222-22-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ27222222-2-2-2-22-2-22-22-2-2-2222-220000000022-2-200000000000000000000
χ28222222-2-2-2-22-2-22-22-2-2-2222-2200000000-2-22200000000000000000000
χ29222222-2-2-2-2-2-2-2-2222-22-2-222-200000000000000002i−2i2i−2i000000000000
χ30222222-2-2-2-2-2-2-2-2222-22-2-222-20000000000000000−2i2i−2i2i000000000000
χ312222-2-222222-2-22-2-22-22-2-22-22000000002-2-2200000000000000000000
χ322222-2-222222-2-22-2-22-22-2-22-2200000000-222-200000000000000000000
χ332222-2-22222-2-2-2-22-2-2-2-22222-200000000000000002i−2i−2i2i000000000000
χ342222-2-22222-2-2-2-22-2-2-2-22222-20000000000000000−2i2i2i−2i000000000000
χ352222-2-222-2-22-2-222222-22-2-2-2-20000000000002i−2i−2i2i0000000000000000
χ362222-2-222-2-22-2-222222-22-2-2-2-2000000000000−2i2i2i−2i0000000000000000
χ372222-2-222-2-2-2-2-2-2-22-222-22-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ382222-2-222-2-2-2-2-2-2-22-222-22-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ392222-2-2-2-2222222-22-2-222-2-22-200000000000000000000000000002-2-22
χ402222-2-2-2-2222222-22-2-222-2-22-20000000000000000000000000000-222-2
χ412222-2-2-2-222-222-2222-2-2-22-2-22000000000000000000002i−2i−2i2i00000000
χ422222-2-2-2-222-222-2222-2-2-22-2-2200000000000000000000−2i2i2i−2i00000000
χ432222-2-2-2-2-2-2-222-2-2-2222222-2-20000000000000000000000002i−2i−2i2i0000
χ442222-2-2-2-2-2-2-222-2-2-2222222-2-2000000000000000000000000−2i2i2i−2i0000
χ4544-4-44-44i−4i0004i−4i000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ4644-4-44-44i−4i0004i−4i00000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ4744-4-44-4−4i4i000−4i4i000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ4844-4-44-4−4i4i000−4i4i00000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ4944-4-4-444i−4i000−4i4i000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ5044-4-4-444i−4i000−4i4i00000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ5144-4-4-44−4i4i0004i−4i000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ5244-4-4-44−4i4i0004i−4i00000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ538-88-8000000800-8000000000000000000000000000000000000000000
χ548-88-8000000-8008000000000000000000000000000000000000000000
χ558-8-8800008-80000000000000000000000000000000000000000000000
χ568-8-880000-880000000000000000000000000000000000000000000000

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