Finite Group Databasebeta

← Group #116367

Character table — Group #116367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ91-1111-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i11-1-111-1-1ii−i−iii−i−i
χ101-1111-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1i−i−iii−i−ii-1-111-1-111ii−i−i−i−iii
χ111-1111-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1−iii−i−iii−i-1-111-1-111−i−iiiii−i−i
χ121-1111-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii11-1-111-1-1−i−iii−i−iii
χ131-1111-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111i−ii−ii−ii−i11-1-1-1-111−i−iii−i−iii
χ141-1111-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111i−i−iii−i−ii-1-11111-1-1−i−iiiii−i−i
χ151-1111-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111−iii−i−iii−i-1-11111-1-1ii−i−i−i−iii
χ161-1111-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111−ii−ii−ii−ii11-1-1-1-111ii−i−iii−i−i
χ172222222222222222-2-2-2-2-2-2-2-200000000000000002-22-2000000000000
χ182222222222222222-2-2-2-2-2-2-2-20000000000000000-22-22000000000000
χ19222222222222-2-2-2-222-2-22-22-200000000002200-2-20000000000000000
χ20222222222222-2-2-2-222-2-22-22-20000000000-2-200220000000000000000
χ21222222222222-2-2-2-2-2-222-22-22000000002200-2-2000000000000000000
χ22222222222222-2-2-2-2-2-222-22-2200000000-2-20022000000000000000000
χ2322222222-2-2-2-222-2-22-22-222-2-2000000000000000000002i−2i2i−2i00000000
χ2422222222-2-2-2-222-2-22-22-222-2-200000000000000000000−2i2i−2i2i00000000
χ2522222222-2-2-2-222-2-2-22-22-2-22222-2-222-2-2000000000000000000000000
χ2622222222-2-2-2-222-2-2-22-22-2-222-2-222-2-222000000000000000000000000
χ2722222222-2-2-2-2-2-2222-2-222-2-220000000000000000000000002-22-20000
χ2822222222-2-2-2-2-2-2222-2-222-2-22000000000000000000000000-22-220000
χ2922222222-2-2-2-2-2-222-222-2-222-200000000000000000000000000002-22-2
χ3022222222-2-2-2-2-2-222-222-2-222-20000000000000000000000000000-22-22
χ312-2222-2-2-222-2-22-22-22-22-2-2-222000000000000000000002i−2i−2i2i00000000
χ322-2222-2-2-222-2-22-22-22-22-2-2-22200000000000000000000−2i2i2i−2i00000000
χ332-2222-2-2-222-2-22-22-2-22-2222-2-222-2-2-2-222000000000000000000000000
χ342-2222-2-2-222-2-22-22-2-22-2222-2-2-2-22222-2-2000000000000000000000000
χ352-2222-2-2-222-2-2-22-222-2-22-222-20000000000000000000000002i−2i−2i2i0000
χ362-2222-2-2-222-2-2-22-222-2-22-222-2000000000000000000000000−2i2i2i−2i0000
χ372-2222-2-2-222-2-2-22-22-222-22-2-2200000000000000000000000000002i−2i−2i2i
χ382-2222-2-2-222-2-2-22-22-222-22-2-220000000000000000000000000000−2i2i2i−2i
χ392-2222-2-2-2-2-2222-2-22-2-2-2-2222200000000000000002-2-22000000000000
χ402-2222-2-2-2-2-2222-2-22-2-2-2-222220000000000000000-222-2000000000000
χ412-2222-2-2-2-2-222-222-222-2-2-22-2200000000002i−2i00−2i2i0000000000000000
χ422-2222-2-2-2-2-222-222-222-2-2-22-220000000000−2i2i002i−2i0000000000000000
χ432-2222-2-2-2-2-222-222-2-2-2222-22-2000000002i−2i00−2i2i000000000000000000
χ442-2222-2-2-2-2-222-222-2-2-2222-22-200000000−2i2i002i−2i000000000000000000
χ45444-4-4-4-444-44-40000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ46444-4-4-4-444-44-4000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ47444-4-4-4-44-44-440000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ48444-4-4-4-44-44-44000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ494-44-4-444-44-4-440000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ504-44-4-444-44-4-44000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ514-44-4-444-4-444-40000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ524-44-4-444-4-444-4000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5388-88-88-8-8000000000000000000000000000000000000000000000000
χ5488-8-88-88-8000000000000000000000000000000000000000000000000
χ558-8-88-8-888000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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