Finite Group Databasebeta

← Group #118626

Character table — Group #118626

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444444416161616161616161616161616161616161616161616161616161616
order12222222224444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91-11-1-111-1-1111-1111-1-1-1-11-1i−ii−i11-1-1i−ii−i11-1-111-1-1ii−i−iii−i−i
χ101-11-1-111-1-1111-1111-1-1-1-11-1i−ii−i-1-111i−ii−i-1-11111-1-1−i−iii−i−iii
χ111-11-1-111-1-1111-1111-1-1-1-11-1i−i−ii11-1-1i−i−ii-1-111-1-111ii−i−i−i−iii
χ121-11-1-111-1-1111-1111-1-1-1-11-1i−i−ii-1-111i−i−ii11-1-1-1-111−i−iiiii−i−i
χ131-11-1-111-1-1111-1111-1-1-1-11-1−iii−i11-1-1−iii−i-1-111-1-111−i−iiiii−i−i
χ141-11-1-111-1-1111-1111-1-1-1-11-1−iii−i-1-111−iii−i11-1-1-1-111ii−i−i−i−iii
χ151-11-1-111-1-1111-1111-1-1-1-11-1−ii−ii11-1-1−ii−ii11-1-111-1-1−i−iii−i−iii
χ161-11-1-111-1-1111-1111-1-1-1-11-1−ii−ii-1-111−ii−ii-1-11111-1-1ii−i−iii−i−i
χ172222222222222-2-2-2-2-2-22-2-20000000000000000000000002-22-2
χ182222222222222-2-2-2-2-2-22-2-2000000000000000000000000-22-22
χ192222222222-2-2-222-22-2-2-2-22000000000000000000002-22-20000
χ202222222222-2-2-222-22-2-2-2-2200000000000000000000-22-220000
χ212222222222-2-2-2-2-22-222-22-200000000000000002-22-200000000
χ222222222222-2-2-2-2-22-222-22-20000000000000000-22-2200000000
χ2322222222-2-22-222-2222-2-2-2-20000000000002i−2i2i−2i000000000000
χ2422222222-2-22-222-2222-2-2-2-2000000000000−2i2i−2i2i000000000000
χ2522222222-2-22-22-22-2-2-22-22222000000-2-2000000000000000000
χ2622222222-2-22-22-22-2-2-22-222-2-200000022000000000000000000
χ2722222222-2-2-22-22-2-22-2222-20022000000-2-20000000000000000
χ2822222222-2-2-22-22-2-22-2222-200-2-2000000220000000000000000
χ2922222222-2-2-22-2-222-22-22-2200002-22-200000000000000000000
χ3022222222-2-2-22-2-222-22-22-220000-22-2200000000000000000000
χ312-22-2-222-22-22-2-22-22-2-222-220000000000002i−2i−2i2i000000000000
χ322-22-2-222-22-22-2-22-22-2-222-22000000000000−2i2i2i−2i000000000000
χ332-22-2-222-22-22-2-2-22-222-222-22i−2i000000−2i2i000000000000000000
χ342-22-2-222-22-22-2-2-22-222-222-2−2i2i0000002i−2i000000000000000000
χ352-22-2-222-22-2-2222-2-2-22-2-222002i−2i000000−2i2i0000000000000000
χ362-22-2-222-22-2-2222-2-2-22-2-22200−2i2i0000002i−2i0000000000000000
χ372-22-2-222-22-2-222-2222-22-2-2-200002-2-2200000000000000000000
χ382-22-2-222-22-2-222-2222-22-2-2-20000-222-200000000000000000000
χ392-22-2-222-2-2222-2-2-2-2222-2-220000000000000000000000002i−2i−2i2i
χ402-22-2-222-2-2222-2-2-2-2222-2-22000000000000000000000000−2i2i2i−2i
χ412-22-2-222-2-22-2-2222-2-2222-2-2000000000000000000002i−2i−2i2i0000
χ422-22-2-222-2-22-2-2222-2-2222-2-200000000000000000000−2i2i2i−2i0000
χ432-22-2-222-2-22-2-22-2-222-2-222200000000000000002-2-2200000000
χ442-22-2-222-2-22-2-22-2-222-2-22220000000000000000-222-200000000
χ45888-8-8-8-88000000000000000000000000000000000000000000
χ4688-88-88-8-8000000000000000000000000000000000000000000
χ4788-8-88-88-8000000000000000000000000000000000000000000
χ488-8888-8-8-8000000000000000000000000000000000000000000
χ498-8-88-8-888000000000000000000000000000000000000000000
χ508-8-8-888-88000000000000000000000000000000000000000000

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