Finite Group Databasebeta

← Group #148481

Character table — Group #148481

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222222222222444444444444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
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
χ91-1-111-1-1111-1-11111-1-1-1-11-1-111111-1-1-1-1ii−i−iii−i−i11-1-11-1i−ii−iii−i−iii−i−i11-1-1
χ101-1-111-1-1111-1-11111-1-1-1-11-1-111111-1-1-1-1ii−i−i−i−iii-1-111-11i−i−iiii−i−i−i−iii-1-111
χ111-1-111-1-1111-1-11111-1-1-1-11-1-111111-1-1-1-1−i−iiiii−i−i-1-111-11−iii−i−i−iiiii−i−i-1-111
χ121-1-111-1-1111-1-11111-1-1-1-11-1-111111-1-1-1-1−i−iii−i−iii11-1-11-1−ii−ii−i−iii−i−iii11-1-1
χ131-1-111-1-1111-1-11111-1-1-1-11-1-11-1-1-1-11111ii−i−iii−i−i11-1-11-1i−ii−i−i−iii−i−iii-1-111
χ141-1-111-1-1111-1-11111-1-1-1-11-1-11-1-1-1-11111ii−i−i−i−iii-1-111-11i−i−ii−i−iiiii−i−i11-1-1
χ151-1-111-1-1111-1-11111-1-1-1-11-1-11-1-1-1-11111−i−iiiii−i−i-1-111-11−iii−iii−i−i−i−iii11-1-1
χ161-1-111-1-1111-1-11111-1-1-1-11-1-11-1-1-1-11111−i−iii−i−iii11-1-11-1−ii−iiii−i−iii−i−i-1-111
χ1722222222222222-2-22-22-2-2-2-2-2000000000000222200000000-2-2000000000000
χ1822222222222222-2-22-22-2-2-2-2-2000000000000-2-2-2-20000000022000000000000
χ19222222222222-2-222-22-22-2-2-2-20000000022220000000000-2-200000000000000
χ20222222222222-2-222-22-22-2-2-2-200000000-2-2-2-200000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-2222200000000000000002222-2-20000000000000000
χ22222222222222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2220000000000000000
χ2322-2-2-22-22-222-22-22-222-2-2-22-22000000000000000000000000002i−2i2i−2i00000000
χ2422-2-2-22-22-222-22-22-222-2-2-22-2200000000000000000000000000−2i2i−2i2i00000000
χ2522-2-2-22-22-222-22-2-222-2-222-22-200000000000000000000000000000000002i−2i2i−2i
χ2622-2-2-22-22-222-22-2-222-2-222-22-20000000000000000000000000000000000−2i2i−2i2i
χ2722-2-2-22-22-222-2-222-2-222-22-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ2822-2-2-22-22-222-2-222-2-222-22-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ2922-2-2-22-22-222-2-22-22-2-222-22-220000000000000000000000000000002-22-20000
χ3022-2-2-22-22-222-2-22-22-2-222-22-22000000000000000000000000000000-22-220000
χ312-22-2-2-222-22-222-22-2-2-222-2-222000000000000000000000000002-2-2200000000
χ322-22-2-2-222-22-222-22-2-2-222-2-22200000000000000000000000000-222-200000000
χ332-22-2-2-222-22-222-2-22-222-222-2-200000000000000000000000000000000002i−2i−2i2i
χ342-22-2-2-222-22-222-2-22-222-222-2-20000000000000000000000000000000000−2i2i2i−2i
χ352-22-2-2-222-22-22-222-22-2-2222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ362-22-2-2-222-22-22-222-22-2-2222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ372-22-2-2-222-22-22-22-2222-2-2-2-2220000000000000000000000000000002i−2i−2i2i0000
χ382-22-2-2-222-22-22-22-2222-2-2-2-222000000000000000000000000000000−2i2i2i−2i0000
χ392-2-222-2-2222-2-222-2-2-22-22-222-20000000000002i2i−2i−2i00000000−2i2i000000000000
χ402-2-222-2-2222-2-222-2-2-22-22-222-2000000000000−2i−2i2i2i000000002i−2i000000000000
χ412-2-222-2-2222-2-2-2-2222-22-2-222-2000000002i2i−2i−2i0000000000−2i2i00000000000000
χ422-2-222-2-2222-2-2-2-2222-22-2-222-200000000−2i−2i2i2i00000000002i−2i00000000000000
χ432-2-222-2-2222-2-2-2-2-2-222222-2-22000000000000000022-2-2-220000000000000000
χ442-2-222-2-2222-2-2-2-2-2-222222-2-220000000000000000-2-2222-20000000000000000
χ4544444444-4-4-4-40000000000002-22-22-22-2000000000000000000000000000000
χ4644444444-4-4-4-4000000000000-22-22-22-22000000000000000000000000000000
χ4744-44-4-44-40000000000000000000000002i−2i2i−2i2-22-22i−2i2i−2i000000000000000000
χ4844-44-4-44-40000000000000000000000002i−2i2i−2i-22-22−2i2i−2i2i000000000000000000
χ4944-44-4-44-4000000000000000000000000−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000
χ5044-44-4-44-4000000000000000000000000−2i2i−2i2i-22-222i−2i2i−2i000000000000000000
χ5144-4-4-44-444-4-440000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ5244-4-4-44-444-4-44000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ534-444-44-4-40000000000000000000000002-2-222i−2i−2i2i−2i2i2i−2i000000000000000000
χ544-444-44-4-40000000000000000000000002-2-22−2i2i2i−2i2i−2i−2i2i000000000000000000
χ554-444-44-4-4000000000000000000000000-222-22i−2i−2i2i2i−2i−2i2i000000000000000000
χ564-444-44-4-4000000000000000000000000-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000
χ574-44-4-4-4444-44-40000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ584-44-4-4-4444-44-4000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ594-4-444-4-44-4-4440000000000002-22-2-22-22000000000000000000000000000000
χ604-4-444-4-44-4-444000000000000-22-222-22-2000000000000000000000000000000
χ61888-88-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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