Finite Group Databasebeta

← Group #455678

Character table — Group #455678

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222222222888888888888888888888888161616161616161616161616161616161616
order12222222222244444444224444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11-111-1-11-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1111-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111111111-11-1-1-1-1-11-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1
χ911111111111111111111-1-11111-1-1-1-1-1-11111111111111-1-1-1-1-11-1-1-1-1-111-1-111
χ1011111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1111-1-11111-1-1
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111
χ1311111111111111111111-1-1-1-1-1-11111-1-1111111111111-1-11111-1-111-1-1-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-11-1-11111-1-111
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-111111111-1-1
χ1722222222-2-2-2-22-2222-2-2-20022-2-2000000000022-2-20000200000-200000000000
χ1822222222-2-2-2-22-2222-2-2-20022-2-20000000000-2-2220000-200000200000000000
χ1922222222-2-2-2-22-2222-2-2-200-2-222000000000022-2-20000-200000200000000000
χ2022222222-2-2-2-22-2222-2-2-200-2-2220000000000-2-2220000200000-200000000000
χ2122222222-2-2-2-2-22-2-2-22222200000000-2-20000000022-2-20200000-20000000000
χ2222222222-2-2-2-2-22-2-2-22222200000000-2-200000000-2-2220-20000020000000000
χ2322222222-2-2-2-2-22-2-2-2222-2-200000000220000000022-2-20-20000020000000000
χ2422222222-2-2-2-2-22-2-2-2222-2-2000000002200000000-2-2220200000-20000000000
χ2522-2-22-22-222-2-22-22-2-222-2002i−2i2i−2i000000000000000000002-200000000002i−2i00
χ2622-2-22-22-222-2-22-22-2-222-2002i−2i2i−2i00000000000000000000-220000000000−2i2i00
χ2722-2-22-22-222-2-22-22-2-222-200−2i2i−2i2i000000000000000000002-20000000000−2i2i00
χ2822-2-22-22-222-2-22-22-2-222-200−2i2i−2i2i00000000000000000000-2200000000002i−2i00
χ2922-2-22-22-222-2-2-22-222-2-222-2000000002-2000000000000000000002i−2i0000002i−2i
χ3022-2-22-22-222-2-2-22-222-2-222-2000000002-200000000000000000000−2i2i000000−2i2i
χ3122-2-22-22-222-2-2-22-222-2-22-2200000000-22000000000000000000002i−2i000000−2i2i
χ3222-2-22-22-222-2-2-22-222-2-22-2200000000-2200000000000000000000−2i2i0000002i−2i
χ3322-2-22-22-2-2-222222-2-2-2-222-22i−2i−2i2i2i2i−2i−2i-22000000000000000000000000000000
χ3422-2-22-22-2-2-222222-2-2-2-222-2−2i2i2i−2i−2i−2i2i2i-22000000000000000000000000000000
χ3522-2-22-22-2-2-222222-2-2-2-22-222i−2i−2i2i−2i−2i2i2i2-2000000000000000000000000000000
χ3622-2-22-22-2-2-222222-2-2-2-22-22−2i2i2i−2i2i2i−2i−2i2-2000000000000000000000000000000
χ372-22-2-2-2222-22-222-22-22-2-20000002i−2i2i−2i002i2i−2i−2i0000000000002-2000000000000
χ382-22-2-2-2222-22-222-22-22-2-20000002i−2i2i−2i00−2i−2i2i2i000000000000-22000000000000
χ392-22-2-2-2222-22-222-22-22-2-2000000−2i2i−2i2i002i2i−2i−2i000000000000-22000000000000
χ402-22-2-2-2222-22-222-22-22-2-2000000−2i2i−2i2i00−2i−2i2i2i0000000000002-2000000000000
χ412-2-22-222-2-222-222-2-22-22-20000002-2-220000000000000000000000002i−2i2i−2i0000
χ422-2-22-222-2-222-222-2-22-22-20000002-2-22000000000000000000000000−2i2i−2i2i0000
χ432-2-22-222-2-222-222-2-22-22-2000000-222-20000000000000000000000002i−2i−2i2i0000
χ442-2-22-222-2-222-222-2-22-22-2000000-222-2000000000000000000000000−2i2i2i−2i0000
χ45444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000
χ4644-44-4-4-440000000000000000000000002i−2i2i−2i22−2200002i2−2i2000000000000000000
χ4744-44-4-4-440000000000000000000000002i−2i2i−2i−22220000−2i22i2000000000000000000
χ4844-44-4-4-44000000000000000000000000−2i2i−2i2i22−220000−2i22i2000000000000000000
χ4944-44-4-4-44000000000000000000000000−2i2i−2i2i−222200002i2−2i2000000000000000000
χ5044-4-44-44-4-4-444-4-4-44444-4000000000000000000000000000000000000000000
χ514-44-4-4-4444-44-4-4-44-44-444000000000000000000000000000000000000000000
χ524-44-4-4-444-44-444-4-44-4-444000000000000000000000000000000000000000000
χ534-44-4-4-444-44-44-444-444-4-4000000000000000000000000000000000000000000
χ544-4-44-444-44-4-444-4-4-444-44000000000000000000000000000000000000000000
χ554-4-44-444-44-4-44-4444-4-44-4000000000000000000000000000000000000000000
χ564-4-44-444-4-444-4-4-444-44-44000000000000000000000000000000000000000000
χ574-4-4-444-440000000000000000000000002-2-220022−2222−2200000000000000000000
χ584-4-4-444-440000000000000000000000002-2-2200−2222−222200000000000000000000
χ594-4-4-444-44000000000000000000000000-222-20022−22−222200000000000000000000
χ604-4-4-444-44000000000000000000000000-222-200−222222−2200000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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