Finite Group Databasebeta

← Group #148482

Character table — Group #148482

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224422222244444444444444444488888888248888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-11111-1-11-1-11-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-1i−ii−i11-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-11111-1-11-1-11-1-11111-1-1-1-111-1-1−i−iii−i−iii1-1−ii−ii11-1-1−i−iii−i−iii
χ111111-1-1-1-111-1-11111-1-11-1-11-1-11111-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii-1-111ii−i−i−i−iii
χ121111-1-1-1-111-1-11111-1-11-1-11-1-11111-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i-1-111−i−iiiii−i−i
χ131111-1-1-1-111-1-11111-1-11-1-11-1-1-1-1-1-1111111-1-1ii−i−iii−i−i1-1i−ii−i-1-111−i−iii−i−iii
χ141111-1-1-1-111-1-11111-1-11-1-11-1-1-1-1-1-1111111-1-1−i−iii−i−iii1-1−ii−ii-1-111ii−i−iii−i−i
χ151111-1-1-1-111-1-11111-1-11-1-11-1-1-1-1-1-11111-1-111ii−i−i−i−iii-11i−i−ii11-1-1−i−iiiii−i−i
χ161111-1-1-1-111-1-11111-1-11-1-11-1-1-1-1-1-11111-1-111−i−iiiii−i−i-11−iii−i11-1-1ii−i−i−i−iii
χ1722222222222222-2-2-2-2-22-2-22-2000000000000000022220000-2-2000000000000
χ1822222222222222-2-2-2-2-22-2-22-20000000000000000-2-2-2-2000022000000000000
χ19222222222222-2-222-2-2-2-22-2-220000000000002222000000-2-200000000000000
χ20222222222222-2-222-2-2-2-22-2-22000000000000-2-2-2-20000002200000000000000
χ21222222222222-2-2-2-2222-2-22-2-200000000222200000000-2-20000000000000000
χ22222222222222-2-2-2-2222-2-22-2-200000000-2-2-2-200000000220000000000000000
χ232222-2-2-2-222-2-222-2-222-2-22-2-2200000000000000002i2i−2i−2i0000−2i2i000000000000
χ242222-2-2-2-222-2-222-2-222-2-22-2-220000000000000000−2i−2i2i2i00002i−2i000000000000
χ252222-2-2-2-222-2-2-2-22222-22-2-22-20000000000002i2i−2i−2i000000−2i2i00000000000000
χ262222-2-2-2-222-2-2-2-22222-22-2-22-2000000000000−2i−2i2i2i0000002i−2i00000000000000
χ272222-2-2-2-222-2-2-2-2-2-2-2-22222220000000022-2-200000000-220000000000000000
χ282222-2-2-2-222-2-2-2-2-2-2-2-222222200000000-2-222000000002-20000000000000000
χ292-2-2222-2-2-222-22-22-22-222-2-2-22000000000000000000000000002i−2i2i−2i00000000
χ302-2-2222-2-2-222-22-22-22-222-2-2-2200000000000000000000000000−2i2i−2i2i00000000
χ312-2-2222-2-2-222-22-2-22-22-2222-2-20000000000000000000000000000002i−2i2i−2i0000
χ322-2-2222-2-2-222-22-2-22-22-2222-2-2000000000000000000000000000000−2i2i−2i2i0000
χ332-2-2222-2-2-222-2-222-2-22-2-2-222200000000000000000000000000000000002-22-2
χ342-2-2222-2-2-222-2-222-2-22-2-2-22220000000000000000000000000000000000-22-22
χ352-2-2222-2-2-222-2-22-222-22-22-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ362-2-2222-2-2-222-2-22-222-22-22-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ372-2-22-2-222-22-222-22-2-222-22-22-2000000000000000000000000002i−2i−2i2i00000000
χ382-2-22-2-222-22-222-22-2-222-22-22-200000000000000000000000000−2i2i2i−2i00000000
χ392-2-22-2-222-22-222-2-222-2-2-2-22220000000000000000000000000000002-2-220000
χ402-2-22-2-222-22-222-2-222-2-2-2-2222000000000000000000000000000000-222-20000
χ412-2-22-2-222-22-22-222-22-2-2222-2-200000000000000000000000000000000002i−2i−2i2i
χ422-2-22-2-222-22-22-222-22-2-2222-2-20000000000000000000000000000000000−2i2i2i−2i
χ432-2-22-2-222-22-22-22-22-2222-2-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ442-2-22-2-222-22-22-22-22-2222-2-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ4544444444-4-4-4-40000000000002-22-22-22-2000000000000000000000000000000
χ4644444444-4-4-4-4000000000000-22-22-22-22000000000000000000000000000000
χ474444-4-4-4-4-4-4440000000000002-22-2-22-22000000000000000000000000000000
χ484444-4-4-4-4-4-444000000000000-22-222-22-2000000000000000000000000000000
χ4944-4-44i−4i4i−4i0000000000000000000000002-22i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000
χ5044-4-44i−4i4i−4i0000000000000000000000002-22i−2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000
χ5144-4-44i−4i4i−4i000000000000000000000000-22−2i2i2ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000
χ5244-4-44i−4i4i−4i000000000000000000000000-22−2i2i−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000
χ5344-4-4−4i4i−4i4i0000000000000000000000002-2−2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000
χ5444-4-4−4i4i−4i4i0000000000000000000000002-2−2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000
χ5544-4-4−4i4i−4i4i000000000000000000000000-222i−2i2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000
χ5644-4-4−4i4i−4i4i000000000000000000000000-222i−2i−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000
χ574-4-4444-4-44-4-440000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ584-4-4444-4-44-4-44000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ594-4-44-4-4444-44-40000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ604-4-44-4-4444-44-4000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
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.