Finite Group Databasebeta

← Group #326642

Character table — Group #326642

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12224444224444444444444488888888888888888822444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1-11-1-1-111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-11-1-1-11-1-1-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-11-111-1-11111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1111-1-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1111-11-1-111-1-111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-22222-2-20000-2-222000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-222000022-2-2000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-22222-2-2000022-2-2000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2220000-2-222000000000000000000000000
χ212222-2-2-2-222-2-20000000022-2-22i2i−2i−2i2i−2i000000002i2i−2i−2i002-20000000000000000
χ222222-2-2-2-222-2-20000000022-2-22i2i−2i−2i2i−2i00000000−2i−2i2i2i00-220000000000000000
χ232222-2-2-2-222-2-20000000022-2-2−2i−2i2i2i−2i2i000000002i2i−2i−2i00-220000000000000000
χ242222-2-2-2-222-2-20000000022-2-2−2i−2i2i2i−2i2i00000000−2i−2i2i2i002-20000000000000000
χ252222-2-2-2-222-2-200000000-2-2222i2i−2i−2i−2i2i2i2i−2i−2i000000000000002-2000000000000
χ262222-2-2-2-222-2-200000000-2-2222i2i−2i−2i−2i2i−2i−2i2i2i00000000000000-22000000000000
χ272222-2-2-2-222-2-200000000-2-222−2i−2i2i2i2i−2i2i2i−2i−2i00000000000000-22000000000000
χ282222-2-2-2-222-2-200000000-2-222−2i−2i2i2i2i−2i−2i−2i2i2i000000000000002-2000000000000
χ292222-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i2-22-200000000000000000002000-200002i−2i00000000
χ302222-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i2-22-20000000000000000000-200020000−2i2i00000000
χ312222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-22-220000000000000000002000-20002i−2i0000000000
χ322222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-22-22000000000000000000-20002000−2i2i0000000000
χ332222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-22-220000000000000000002000-2000−2i2i0000000000
χ342222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-22-22000000000000000000-200020002i−2i0000000000
χ352222-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i2-22-200000000000000000002000-20000−2i2i00000000
χ362222-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i2-22-20000000000000000000-2000200002i−2i00000000
χ372-2-2222-2-2-22-222i−2i2i−2i000000002i−2i2i−2i000000002-20000000000000000i2−i22−22−2i2−i2
χ382-2-2222-2-2-22-222i−2i2i−2i000000002i−2i2i−2i000000002-20000000000000000−i2i2−22−22−i2i2
χ392-2-2222-2-2-22-222i−2i2i−2i00000000−2i2i−2i2i00000000-220000000000000000i2−i22−2−22−i2i2
χ402-2-2222-2-2-22-222i−2i2i−2i00000000−2i2i−2i2i00000000-220000000000000000−i2i2−222−2i2−i2
χ412-2-2222-2-2-22-22−2i2i−2i2i000000002i−2i2i−2i00000000-220000000000000000i2−i2−222−2−i2i2
χ422-2-2222-2-2-22-22−2i2i−2i2i000000002i−2i2i−2i00000000-220000000000000000−i2i22−2−22i2−i2
χ432-2-2222-2-2-22-22−2i2i−2i2i00000000−2i2i−2i2i000000002-20000000000000000i2−i2−22−22i2−i2
χ442-2-2222-2-2-22-22−2i2i−2i2i00000000−2i2i−2i2i000000002-20000000000000000−i2i22−22−2−i2i2
χ4544444444-4-4-4-4000000004-4-4400000000000000000000000000000000000000
χ4644444444-4-4-4-400000000-444-400000000000000000000000000000000000000
χ4744-4-44i−4i4i−4i000000002+2i−2−2i2−2i−2+2i00000000002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4844-4-44i−4i4i−4i000000002+2i−2−2i2−2i−2+2i0000000000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4944-4-44i−4i4i−4i00000000−2−2i2+2i−2+2i2−2i00000000002ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ300000000000000000000
χ5044-4-44i−4i4i−4i00000000−2−2i2+2i−2+2i2−2i0000000000−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5144-4-4−4i4i−4i4i000000002−2i−2+2i2+2i−2−2i00000000002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ00000000000000000000
χ5244-4-4−4i4i−4i4i000000002−2i−2+2i2+2i−2−2i0000000000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5344-4-4−4i4i−4i4i00000000−2+2i2−2i−2−2i2+2i00000000002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5444-4-4−4i4i−4i4i00000000−2+2i2−2i−2−2i2+2i0000000000−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ00000000000000000000
χ554-4-4444-4-44-44-400000000000000000000004-400000000000000000000000000
χ564-4-4444-4-44-44-40000000000000000000000-4400000000000000000000000000
χ574-4-44-4-4444-4-444-4-440000000000000000000000000000000000000000000000
χ584-4-44-4-4444-4-44-444-40000000000000000000000000000000000000000000000
χ594-4-44-4-444-444-40000000000004-4-440000000000000000000000000000000000
χ604-4-44-4-444-444-4000000000000-444-40000000000000000000000000000000000
χ618-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000

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