Finite Group Databasebeta

← Group #129462

Character table — Group #129462

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12222244442244444444444444444444442444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-22222-2-2-2-222-2-222-2-200000000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000
χ21222222-2-2-2-222-2-222-2-222-2-2000000000000002-22-20000000000000000
χ22222222-2-2-2-222-2-222-2-222-2-200000000000000-22-220000000000000000
χ23222222-2-2-2-222-2-2-2-222-2-222000000000000002-2-220000000000000000
χ24222222-2-2-2-222-2-2-2-222-2-22200000000000000-222-20000000000000000
χ25222222-2-2-2-2-2-22222-2-2-2-2220000000022-2-22-200000000000000000000
χ26222222-2-2-2-2-2-22222-2-2-2-22200000000-2-222-2200000000000000000000
χ27222222-2-2-2-2-2-222-2-22222-2-20000000022-2-2-2200000000000000000000
χ28222222-2-2-2-2-2-222-2-22222-2-200000000-2-2222-200000000000000000000
χ292-2-222-222-2-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ302-2-222-222-2-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ312-2-222-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ322-2-222-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ332-2-222-222-2-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ342-2-222-222-2-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ352-2-222-222-2-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ362-2-222-222-2-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ372-2-222-2-2-2222-2-222i−2i−2i2i2i−2i−2i2i0000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ382-2-222-2-2-2222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ392-2-222-2-2-2222-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ402-2-222-2-2-2222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ412-2-222-2-2-222-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ422-2-222-2-2-222-222-22i−2i−2i2i−2i2i2i−2i0000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ432-2-222-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ442-2-222-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ454444-4-44-44-4000000000000004-4000000000000000000000000000000
χ464444-4-44-44-400000000000000-44000000000000000000000000000000
χ474444-4-4-44-440000000000004-400000000000000000000000000000000
χ484444-4-4-44-44000000000000-4400000000000000000000000000000000
χ494-4-44-444-4-4400000000000000004-40000000000000000000000000000
χ504-4-44-444-4-440000000000000000-440000000000000000000000000000
χ514-4-44-44-444-40000000000000000004-400000000000000000000000000
χ524-4-44-44-444-4000000000000000000-4400000000000000000000000000
χ5388-8-8000000000000000000000000004-4000000000000000000000000
χ5488-8-800000000000000000000000000-44000000000000000000000000
χ558-88-800000000000000000000000000004-40000000000000000000000
χ568-88-80000000000000000000000000000-440000000000000000000000

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