Finite Group Databasebeta

← Group #129456

Character table — Group #129456

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order12222222222222444444444444444444224444448888888888888888
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
χ5111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-11-11-1-111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-11-11-1-111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-1111111111111-1-1-1-1-1-11-11-1-1-11111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-1111111111111-1-1-1-1-1-11-11-1-1-111-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-1111111111111-1-1-1-1-1-1-11-1111-1-111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-1111111111111-1-1-1-1-1-1-11-1111-1-1-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-22222-2-2-2-2-2-222-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000
χ2122222-2-2-2-22000022-2-222-2-222-2-2000000020-22-2000000000000000000
χ2222222-2-2-2-22000022-2-222-2-222-2-20000000-202-22000000000000000000
χ2322222-2-2-2-22000022-2-2-2-222-2-222000000020-2-22000000000000000000
χ2422222-2-2-2-22000022-2-2-2-222-2-2220000000-2022-2000000000000000000
χ2522222-2-2-2-220000-2-22222-2-2-2-22200000020-20002-20000000000000000
χ2622222-2-2-2-220000-2-22222-2-2-2-222000000-202000-220000000000000000
χ2722222-2-2-2-220000-2-222-2-22222-2-200000020-2000-220000000000000000
χ2822222-2-2-2-220000-2-222-2-22222-2-2000000-2020002-20000000000000000
χ292-22-2222-2-2-200002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000002ζ3−2ζ3002ζ−2ζ
χ302-22-2222-2-2-200002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000−2ζ32ζ300−2ζ2ζ
χ312-22-2222-2-2-200002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000002ζ−2ζ002ζ3−2ζ3
χ322-22-2222-2-2-200002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2ζ2ζ00−2ζ32ζ3
χ332-22-2222-2-2-20000-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000002ζ−2ζ002ζ3−2ζ300
χ342-22-2222-2-2-20000-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000−2ζ2ζ00−2ζ32ζ300
χ352-22-2222-2-2-20000-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000002ζ3−2ζ3002ζ−2ζ00
χ362-22-2222-2-2-20000-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000−2ζ32ζ300−2ζ2ζ00
χ372-22-22-2-222-200002-2-222i−2i−2i2i2i−2i−2i2i000000000000002ζ−2ζ002ζ3−2ζ30000000000
χ382-22-22-2-222-200002-2-222i−2i−2i2i2i−2i−2i2i00000000000000−2ζ2ζ00−2ζ32ζ30000000000
χ392-22-22-2-222-200002-2-22−2i2i2i−2i−2i2i2i−2i000000000000002ζ3−2ζ3002ζ−2ζ0000000000
χ402-22-22-2-222-200002-2-22−2i2i2i−2i−2i2i2i−2i00000000000000−2ζ32ζ300−2ζ2ζ0000000000
χ412-22-22-2-222-20000-222-22i−2i−2i2i−2i2i2i−2i00000000000000002ζ−2ζ002ζ3−2ζ300000000
χ422-22-22-2-222-20000-222-22i−2i−2i2i−2i2i2i−2i0000000000000000−2ζ2ζ00−2ζ32ζ300000000
χ432-22-22-2-222-20000-222-2−2i2i2i−2i2i−2i−2i2i00000000000000002ζ3−2ζ3002ζ−2ζ00000000
χ442-22-22-2-222-20000-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000−2ζ32ζ300−2ζ2ζ00000000
χ454444-44-44-4-4000000000000000000004-4000000000000000000000000
χ464444-44-44-4-400000000000000000000-44000000000000000000000000
χ474444-4-44-44-40000000000000000004-400000000000000000000000000
χ484444-4-44-44-4000000000000000000-4400000000000000000000000000
χ494-44-4-44-4-44444-4-4000000000000000000000000000000000000000000
χ504-44-4-44-4-444-4-444000000000000000000000000000000000000000000
χ514-44-4-4-444-4400000000000000004-40000000000000000000000000000
χ524-44-4-4-444-440000000000000000-440000000000000000000000000000
χ5388-8-80000004-44-4000000000000000000000000000000000000000000
χ5488-8-8000000-44-44000000000000000000000000000000000000000000
χ558-8-880000004-4-44000000000000000000000000000000000000000000
χ568-8-88000000-444-4000000000000000000000000000000000000000000

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