Finite Group Databasebeta

← Group #119404

Character table — Group #119404

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111111111111144444444444488888888888888888888888816161616161616161616161616161616
order12222222444444442244444444444444444488888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-11111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-11111-1-1ii−i−i−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1-1-111ii−i−iii−i−i
χ1722222222222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000002-22-2
χ1822222222222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000-22-22
χ192222222222222222-2-2-2-222-22-2-2-22000000000000000000000000000000002-22-20000
χ202222222222222222-2-2-2-222-22-2-2-2200000000000000000000000000000000-22-220000
χ212222222222222222-2-2-2-2-2-22-2222-20000000000000000000000002-22-2000000000000
χ222222222222222222-2-2-2-2-2-22-2222-2000000000000000000000000-22-22000000000000
χ2322222222-2-2-2-2-2-2-2-222-2-222-2-222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ2422222222-2-2-2-2-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2220000000000000000000000002-2-22000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222000000000000000000000000-222-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2-2222-220000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2-2222-22000000000000000000000000000000000000−2i2i2i−2i
χ292-2-2222-2-222-2-2-2-2222-22-22-22-22-2-2200000000000000000000000000002i−2i2i−2i00000000
χ302-2-2222-2-222-2-2-2-2222-22-22-22-22-2-220000000000000000000000000000−2i2i−2i2i00000000
χ312-2-2222-2-222-2-2-2-2222-22-2-22-22-222-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ322-2-2222-2-222-2-2-2-2222-22-2-22-22-222-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ332-2-2222-2-222-2-2-2-222-22-222-2-2-2-22220000000022-2-222-2-2000000000000000000000000
χ342-2-2222-2-222-2-2-2-222-22-222-2-2-2-222200000000-2-222-2-222000000000000000000000000
χ352-2-2222-2-222-2-2-2-222-22-22-22222-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ362-2-2222-2-222-2-2-2-222-22-22-22222-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ372-2-2222-2-2-2-22222-2-22-2-222-2-222-22-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ382-2-2222-2-2-2-22222-2-22-2-222-2-222-22-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ392-2-2222-2-2-2-22222-2-22-2-22-222-2-22-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402-2-2222-2-2-2-22222-2-22-2-22-222-2-22-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412-2-2222-2-2-2-22222-2-2-222-22-222-22-2-200000000000000000000000000002i−2i−2i2i00000000
χ422-2-2222-2-2-2-22222-2-2-222-22-222-22-2-20000000000000000000000000000−2i2i2i−2i00000000
χ432-2-2222-2-2-2-22222-2-2-222-2-22-2-22-22222-2-2-2-22200000000000000000000000000000000
χ442-2-2222-2-2-2-22222-2-2-222-2-22-2-22-222-2-22222-2-200000000000000000000000000000000
χ454444-4-4-4-44444-4-4-4-40000000000002-22-22-22-200000000000000000000000000000000
χ464444-4-4-4-44444-4-4-4-4000000000000-22-22-22-2200000000000000000000000000000000
χ474444-4-4-4-4-4-4-4-444440000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ484444-4-4-4-4-4-4-4-44444000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ4944-4-44-44-44i−4i4i−4i4i−4i4i−4i000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ5044-4-44-44-44i−4i4i−4i4i−4i4i−4i00000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ5144-4-44-44-4−4i4i−4i4i−4i4i−4i4i000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ5244-4-44-44-4−4i4i−4i4i−4i4i−4i4i00000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ5344-4-4-44-444i−4i4i−4i−4i4i−4i4i00000000000000000000000000002i−2i2i−2i2-22-20000000000000000
χ5444-4-4-44-444i−4i4i−4i−4i4i−4i4i0000000000000000000000000000−2i2i−2i2i-22-220000000000000000
χ5544-4-4-44-44−4i4i−4i4i4i−4i4i−4i00000000000000000000000000002i−2i2i−2i-22-220000000000000000
χ5644-4-4-44-44−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000−2i2i−2i2i2-22-20000000000000000
χ574-44-44-4-444i−4i−4i4i−4i4i4i−4i000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ584-44-44-4-444i−4i−4i4i−4i4i4i−4i00000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ594-44-44-4-44−4i4i4i−4i4i−4i−4i4i000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ604-44-44-4-44−4i4i4i−4i4i−4i−4i4i00000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ614-44-4-444-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ624-44-4-444-44i−4i−4i4i4i−4i−4i4i0000000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ634-44-4-444-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ644-44-4-444-4−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ654-4-44-4-44444-4-444-4-40000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ664-4-44-4-44444-4-444-4-4000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ674-4-44-4-444-4-444-4-4440000000000002-2-22-222-200000000000000000000000000000000
χ684-4-44-4-444-4-444-4-444000000000000-222-22-2-2200000000000000000000000000000000

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