Finite Group Databasebeta

← Group #149321

Character table — Group #149321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12224444224422222244444444444444448888888844444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1
χ911111111111111-1-1-1-111-1-11111-1-111-1-1-1-111111111ii−i−iii−i−i-1-1-1-1ii−i−iii−i−i
χ1011111111111111-1-1-1-111-1-11111-1-111-1-1-1-111111111−i−iii−i−iii-1-1-1-1−i−iii−i−iii
χ1111111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii1111ii−i−i−i−iii
χ1211111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i1111−i−iiiii−i−i
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i11-1-1−i−iii−i−iii
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii11-1-1ii−i−iii−i−i
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii-1-111−i−iiiii−i−i
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i-1-111ii−i−i−i−iii
χ17222222222222-2-22-22-2-2-22-222222-2-2-222-2-20000000000000000000000000000
χ18222222222222-2-22-22-2-2-22-2-2-2-2-22-222-2-2220000000000000000000000000000
χ19222222222222-2-2-22-22-2-2-222222-22-2-2-2-2220000000000000000000000000000
χ20222222222222-2-2-22-22-2-2-22-2-2-2-2-222222-2-20000000000000000000000000000
χ212222-2-2-2-222-2-2222-22-2-2-2-220000-220000002i2i−2i−2i000000000000002i−2i00000000
χ222222-2-2-2-222-2-2222-22-2-2-2-220000-22000000−2i−2i2i2i00000000000000−2i2i00000000
χ232222-2-2-2-222-2-222-22-22-2-22-200002-20000002i2i−2i−2i00000000000000−2i2i00000000
χ242222-2-2-2-222-2-222-22-22-2-22-200002-2000000−2i−2i2i2i000000000000002i−2i00000000
χ252222-2-2-2-222-2-2-2-2222222-2-20000-2-200000000002i2i−2i−2i000000002i−2i0000000000
χ262222-2-2-2-222-2-2-2-2222222-2-20000-2-20000000000−2i−2i2i2i00000000−2i2i0000000000
χ272222-2-2-2-222-2-2-2-2-2-2-2-2222200002200000000002i2i−2i−2i00000000−2i2i0000000000
χ282222-2-2-2-222-2-2-2-2-2-2-2-222220000220000000000−2i−2i2i2i000000002i−2i0000000000
χ292-2-2222-2-22-22-22-222-2-22-22-20000-220000000000000000000000000000002-22-2
χ302-2-2222-2-22-22-22-222-2-22-22-20000-22000000000000000000000000000000-22-22
χ312-2-2222-2-22-22-22-2-2-2222-2-2200002-20000000000000000000000000000002i−2i−2i2i
χ322-2-2222-2-22-22-22-2-2-2222-2-2200002-2000000000000000000000000000000−2i2i2i−2i
χ332-2-2222-2-22-22-2-222-2-22-22220000-2-20000000000000000002-22-2000000000000
χ342-2-2222-2-22-22-2-222-2-22-22220000-2-2000000000000000000-22-22000000000000
χ352-2-2222-2-22-22-2-22-222-2-22-2-20000220000000000000000002i−2i−2i2i000000000000
χ362-2-2222-2-22-22-2-22-222-2-22-2-2000022000000000000000000−2i2i2i−2i000000000000
χ372-2-22-2-2222-2-222-22-2-22-22-2-2000022000000000000000000000000002-22-20000
χ382-2-22-2-2222-2-222-22-2-22-22-2-200002200000000000000000000000000-22-220000
χ392-2-22-2-2222-2-222-2-222-2-22220000-2-2000000000000000000000000002i−2i−2i2i0000
χ402-2-22-2-2222-2-222-2-222-2-22220000-2-200000000000000000000000000−2i2i2i−2i0000
χ412-2-22-2-2222-2-22-2222-2-22-2-2200002-2000000000000002i−2i2i−2i0000000000000000
χ422-2-22-2-2222-2-22-2222-2-22-2-2200002-200000000000000−2i2i−2i2i0000000000000000
χ432-2-22-2-2222-2-22-22-2-2222-22-20000-22000000000000002-2-220000000000000000
χ442-2-22-2-2222-2-22-22-2-2222-22-20000-2200000000000000-222-20000000000000000
χ4544444444-4-4-4-400000000000000004i−4i00000000000000000000000000000000
χ4644444444-4-4-4-40000000000000000−4i4i00000000000000000000000000000000
χ474444-4-4-4-4-4-44400000000004i4i−4i−4i000000000000000000000000000000000000
χ484444-4-4-4-4-4-4440000000000−4i−4i4i4i000000000000000000000000000000000000
χ4944-4-44i−4i4i−4i000000000000002+2i−2−2i2−2i−2+2i000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000000000
χ5044-4-44i−4i4i−4i000000000000002+2i−2−2i2−2i−2+2i00000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000
χ5144-4-44i−4i4i−4i00000000000000−2−2i2+2i−2+2i2−2i000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ300000000000000000000
χ5244-4-44i−4i4i−4i00000000000000−2−2i2+2i−2+2i2−2i00000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ300000000000000000000
χ5344-4-4−4i4i−4i4i000000000000002−2i−2+2i2+2i−2−2i000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000
χ5444-4-4−4i4i−4i4i000000000000002−2i−2+2i2+2i−2−2i00000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5544-4-4−4i4i−4i4i00000000000000−2+2i2−2i−2−2i2+2i000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5644-4-4−4i4i−4i4i00000000000000−2+2i2−2i−2−2i2+2i00000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000
χ574-4-4444-4-4-44-440000000000000000004-4000000000000000000000000000000
χ584-4-4444-4-4-44-44000000000000000000-44000000000000000000000000000000
χ594-4-44-4-444-444-4000000000000000000004-40000000000000000000000000000
χ604-4-44-4-444-444-400000000000000000000-440000000000000000000000000000
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.