Finite Group Databasebeta

← Group #136000

Character table — Group #136000

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224422222244444444448888888888888888448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111ii−i−iii−i−iii−i−iii−i−i1-1ii−i−iii−i−i11-1-111-1-1
χ101111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111ii−i−iii−i−iii−i−iii−i−i1-1−i−iii−i−iii-1-111-1-111
χ111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111−i−iii−i−iii−i−iii−i−iii1-1ii−i−iii−i−i-1-111-1-111
χ121111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111−i−iii−i−iii−i−iii−i−iii1-1−i−iii−i−iii11-1-111-1-1
χ131111-1-1-1-111-1-111-1-1-1-1-11111-1-1-111ii−i−i−i−iiiii−i−i−i−iii-11ii−i−i−i−iii11-1-1-1-111
χ141111-1-1-1-111-1-111-1-1-1-1-11111-1-1-111ii−i−i−i−iiiii−i−i−i−iii-11−i−iiiii−i−i-1-11111-1-1
χ151111-1-1-1-111-1-111-1-1-1-1-11111-1-1-111−i−iiiii−i−i−i−iiiii−i−i-11ii−i−i−i−iii-1-11111-1-1
χ161111-1-1-1-111-1-111-1-1-1-1-11111-1-1-111−i−iiiii−i−i−i−iiiii−i−i-11−i−iiiii−i−i11-1-1-1-111
χ17222222222222222222222222-2-2-2-20000000000000000-2-20000000000000000
χ1822222222222222-2-2-2-22-2-2-2-22-2-2-2-20000000000000000220000000000000000
χ19222222222222-2-20000-20000-22-22-2000022220000-2-2-2-2000000000000000000
χ20222222222222-2-20000-20000-22-22-20000-2-2-2-200002222000000000000000000
χ21222222222222-2-20000-20000-2-22-2222220000-2-2-2-20000000000000000000000
χ22222222222222-2-20000-20000-2-22-22-2-2-2-2000022220000000000000000000000
χ232222-2-2-2-222-2-2222222-2-2-2-2-2-222-2-20000000000000000-220000000000000000
χ242222-2-2-2-222-2-222-2-2-2-2-22222-222-2-200000000000000002-20000000000000000
χ252222-2-2-2-222-2-2-2-200002000022-2-222i2i−2i−2i0000−2i−2i2i2i0000000000000000000000
χ262222-2-2-2-222-2-2-2-200002000022-2-22−2i−2i2i2i00002i2i−2i−2i0000000000000000000000
χ272222-2-2-2-222-2-2-2-20000200002-222-200002i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ282222-2-2-2-222-2-2-2-20000200002-222-20000−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ292-2-2222-2-22-22-22-222-2-2-222-2-22000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-2-2222-2-22-22-22-222-2-2-222-2-22000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-2-2222-2-22-22-22-2-2-222-2-2-2222000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-2-2222-2-22-22-22-2-2-222-2-2-2222000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-22-2-2222-2-222-222-2-22-2-222-2000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ342-2-22-2-2222-2-222-222-2-22-2-222-2000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ352-2-22-2-2222-2-222-2-2-222222-2-2-2000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ362-2-22-2-2222-2-222-2-2-222222-2-2-2000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3744444444-4-4-4-400000000000000000000000000000000002-22-2000000000000
χ3844444444-4-4-4-40000000000000000000000000000000000-22-22000000000000
χ394444-4-4-4-4-4-44400000000000000000000000000000000002i−2i−2i2i000000000000
χ404444-4-4-4-4-4-4440000000000000000000000000000000000−2i2i2i−2i000000000000
χ4144-4-44i−4i4i−4i0000002-22-202i−2i2i−2i000002ζ−2ζ2ζ3−2ζ3000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4244-4-44i−4i4i−4i0000002-22-202i−2i2i−2i00000−2ζ2ζ−2ζ32ζ300000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ4344-4-44i−4i4i−4i000000-22-220−2i2i−2i2i000002ζ−2ζ2ζ3−2ζ300000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ4444-4-44i−4i4i−4i000000-22-220−2i2i−2i2i00000−2ζ2ζ−2ζ32ζ3000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4544-4-4−4i4i−4i4i0000002-22-20−2i2i−2i2i000002ζ3−2ζ32ζ−2ζ000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ4644-4-4−4i4i−4i4i0000002-22-20−2i2i−2i2i00000−2ζ32ζ3−2ζ2ζ00000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ4744-4-4−4i4i−4i4i000000-22-2202i−2i2i−2i000002ζ3−2ζ32ζ−2ζ00000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ4844-4-4−4i4i−4i4i000000-22-2202i−2i2i−2i00000−2ζ32ζ3−2ζ2ζ000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ494-44-44i−4i−4i4i0000002-2-2202i−2i−2i2i0000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000
χ504-44-44i−4i−4i4i0000002-2-2202i−2i−2i2i000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ514-44-44i−4i−4i4i000000-222-20−2i2i2i−2i0000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ524-44-44i−4i−4i4i000000-222-20−2i2i2i−2i000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000
χ534-44-4−4i4i4i−4i0000002-2-220−2i2i2i−2i0000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000
χ544-44-4−4i4i4i−4i0000002-2-220−2i2i2i−2i000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000
χ554-44-4−4i4i4i−4i000000-222-202i−2i−2i2i0000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000
χ564-44-4−4i4i4i−4i000000-222-202i−2i−2i2i000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000
χ574-4-4444-4-44-44-4-44000040000-400000000000000000000000000000000000000
χ584-4-4444-4-4-44-44000000000000000000000000000000000000002-22-200000000
χ594-4-4444-4-4-44-4400000000000000000000000000000000000000-22-2200000000
χ604-4-44-4-4444-4-44-440000-40000400000000000000000000000000000000000000
χ614-4-44-4-444-444-4000000000000000000000000000000000000002i−2i−2i2i00000000
χ624-4-44-4-444-444-400000000000000000000000000000000000000−2i2i2i−2i00000000

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