Finite Group Databasebeta

← Group #148166

Character table — Group #148166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222222222222444422224444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ911-1-1-111-11-11-1111-1-1-11-111-1-111-1-111-1-111-1-1ii−i−iii−i−ii−i1-1i−i11-1-1ii−i−iii−i−i
χ1011-1-1-111-11-11-1111-1-1-11-111-1-111-1-111-1-111-1-1−i−iii−i−iii−ii1-1−ii11-1-1−i−iii−i−iii
χ1111-1-1-111-11-11-1111-1-1-11-111-1-111-1-1-1-11111-1-1ii−i−i−i−iii−ii-11i−i-1-111ii−i−i−i−iii
χ1211-1-1-111-11-11-1111-1-1-11-111-1-111-1-1-1-11111-1-1−i−iiiii−i−ii−i-11−ii-1-111−i−iiiii−i−i
χ1311-1-1-111-11-11-1111-1-1-11-111-1-1-1-11111-1-1-1-111ii−i−iii−i−ii−i1-1i−i-1-111−i−iii−i−iii
χ1411-1-1-111-11-11-1111-1-1-11-111-1-1-1-11111-1-1-1-111−i−iii−i−iii−ii1-1−ii-1-111ii−i−iii−i−i
χ1511-1-1-111-11-11-1111-1-1-11-111-1-1-1-111-1-111-1-111ii−i−i−i−iii−ii-11i−i11-1-1−i−iiiii−i−i
χ1611-1-1-111-11-11-1111-1-1-11-111-1-1-1-111-1-111-1-111−i−iiiii−i−ii−i-11−ii11-1-1ii−i−i−i−iii
χ1722222222222222-22-2-2-22-2-2-2-2000000000000222200000000-2-2000000000000
χ1822222222222222-22-2-2-22-2-2-2-2000000000000-2-2-2-20000000022000000000000
χ19222222222222-2-22-2222-2-2-2-2-20000222200000000000000-2-200000000000000
χ20222222222222-2-22-2222-2-2-2-2-20000-2-2-2-2000000000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-2222200000000000000002222-2-20000000000000000
χ22222222222222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2220000000000000000
χ2322-2-2-222-22-22-222-2-222-2-2-2-2220000000000002i2i−2i−2i00000000−2i2i000000000000
χ2422-2-2-222-22-22-222-2-222-2-2-2-222000000000000−2i−2i2i2i000000002i−2i000000000000
χ2522-2-2-222-22-22-2-2-222-2-222-2-222000022-2-200000000000000-2200000000000000
χ2622-2-2-222-22-22-2-2-222-2-222-2-2220000-2-222000000000000002-200000000000000
χ2722-2-2-222-22-22-2-2-2-2222-2222-2-200000000000000002i2i−2i−2i−2i2i0000000000000000
χ2822-2-2-222-22-22-2-2-2-2222-2222-2-20000000000000000−2i−2i2i2i2i−2i0000000000000000
χ292-222-2-22-222-2-22-2222-2-2-22-22-22-22-200002-22-200000000000000000000000000
χ302-222-2-22-222-2-22-2222-2-2-22-22-2-22-220000-22-2200000000000000000000000000
χ312-222-2-22-222-2-22-2-22-222-2-22-220000000000000000000000000000002i−2i2i−2i0000
χ322-222-2-22-222-2-22-2-22-222-2-22-22000000000000000000000000000000−2i2i−2i2i0000
χ332-222-2-22-222-2-2-222-22-2-22-22-22000000000000000000000000002i−2i2i−2i00000000
χ342-222-2-22-222-2-2-222-22-2-22-22-2200000000000000000000000000−2i2i−2i2i00000000
χ352-222-2-22-222-2-2-22-2-2-22222-22-200000000000000000000000000000000002i−2i2i−2i
χ362-222-2-22-222-2-2-22-2-2-22222-22-20000000000000000000000000000000000−2i2i−2i2i
χ372-2-2-22-2222-2-222-22-2-22-222-2-222-2-2200002-2-2200000000000000000000000000
χ382-2-2-22-2222-2-222-22-2-22-222-2-22-222-20000-222-200000000000000000000000000
χ392-2-2-22-2222-2-222-2-2-22-222-222-20000000000000000000000000000002-2-220000
χ402-2-2-22-2222-2-222-2-2-22-222-222-2000000000000000000000000000000-222-20000
χ412-2-2-22-2222-2-22-2222-22-2-2-222-2000000000000000000000000002i−2i−2i2i00000000
χ422-2-2-22-2222-2-22-2222-22-2-2-222-200000000000000000000000000−2i2i2i−2i00000000
χ432-2-2-22-2222-2-22-22-222-22-22-2-2200000000000000000000000000000000002-2-22
χ442-2-2-22-2222-2-22-22-222-22-22-2-220000000000000000000000000000000000-222-2
χ4544444444-4-4-4-400000000000022220000-2-2-2-200000000000000000000000000
χ4644444444-4-4-4-4000000000000-2-2-2-20000222200000000000000000000000000
χ4744-4-4-444-4-44-4400000000000022-2-20000-2-22200000000000000000000000000
χ4844-4-4-444-4-44-44000000000000-2-222000022-2-200000000000000000000000000
χ494-444-4-44-4-4-4440000000000002-22-20000-22-2200000000000000000000000000
χ504-444-4-44-4-4-444000000000000-22-2200002-22-200000000000000000000000000
χ514-44-444-4-4000000000000000000002-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000
χ524-44-444-4-4000000000000000000002-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ534-44-444-4-400000000000000000000-22-2200002i−2i2i−2i−2i2i−2i2i000000000000000000
χ544-44-444-4-400000000000000000000-22-220000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ554-4-44-44-44000000000000000000002-2-2200002-2-222-2-22000000000000000000
χ564-4-44-44-44000000000000000000002-2-220000-222-2-222-2000000000000000000
χ574-4-44-44-4400000000000000000000-222-200002-2-22-222-2000000000000000000
χ584-4-44-44-4400000000000000000000-222-20000-222-22-2-22000000000000000000
χ594-4-4-44-444-444-40000000000002-2-220000-222-200000000000000000000000000
χ604-4-4-44-444-444-4000000000000-222-200002-2-2200000000000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ6288-888-8-8-8000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).