Finite Group Databasebeta

← Group #171973

Character table — Group #171973

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ911111111-1-1-1-11-1-11-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-111-1-11-11-11-111-1-111-1-1
χ1011111111-1-1-1-11-1-11-1-1-1-1111111-1-111-1-111-1-1-1-1-1-11111-1-1111-11-11-1-1-111-1-111
χ1111111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1111-1-11-1111-1-1-1-111
χ1211111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111111-1-11-1-11-11-1-11111-1-1
χ1311111111-1-1-1-11-1-11-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-11111-1-1
χ1411111111-1-1-1-11-1-11-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1111111-1-1-111-1-1111-1-1-1-111
χ1511111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-111-1-1-11-111-1-1-111-1-111
χ1611111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-111-11-111-111-1-111-1-1
χ172222222222222-2-2-222-2-2-2-22-200002222000000000000000000-2-20000000000
χ182222222222222-2-2-222-2-2-2-22-20000-2-2-2-2000000000000000000220000000000
χ19222222222222-2222-2-2-2-2-2-2-22222200000000000000000000-2-2000000000000
χ20222222222222-2222-2-2-2-2-2-2-22-2-2-2-20000000000000000000022000000000000
χ21222222222222-2-2-2-2-2-22222-2-20000000022-2-20000000000000000-2200000000
χ22222222222222-2-2-2-2-2-22222-2-200000000-2-22200000000000000002-200000000
χ2322222222-2-2-2-2222-2-2-222-2-22-2000022-2-2000000000000000000-220000000000
χ2422222222-2-2-2-2222-2-2-222-2-22-20000-2-2220000000000000000002-20000000000
χ2522222222-2-2-2-2-222-222-2-222-2-20000000022220000000000000000-2-200000000
χ2622222222-2-2-2-2-222-222-2-222-2-200000000-2-2-2-200000000000000002200000000
χ2722222222-2-2-2-2-2-2-222222-2-2-2222-2-200000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-222222-2-2-22-2-222000000000000000000002-2000000000000
χ2922-222-2-2-222-2-202-2-2000000022-22-200000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i20000
χ3022-222-2-2-222-2-202-2-2000000022-22-200000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i20000
χ3122-222-2-2-222-2-202-2-200000002-22-2200000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i20000
χ3222-222-2-2-222-2-202-2-200000002-22-2200000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i20000
χ3322-222-2-2-2-2-2220-22-2000000022-2-2200000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i20000
χ3422-222-2-2-2-2-2220-22-2000000022-2-2200000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i20000
χ3522-222-2-2-2-2-2220-22-200000002-222-200000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i20000
χ3622-222-2-2-2-2-2220-22-200000002-222-200000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i20000
χ372-222-22-2-22-22-2-20002-200002000002-22-20000i2−i2i2−i2i2−i2i2−i200000000000000i2−i2i2−i2
χ382-222-22-2-22-22-2-20002-200002000002-22-20000−i2i2−i2i2−i2i2−i2i200000000000000−i2i2−i2i2
χ392-222-22-2-22-22-2-20002-20000200000-22-220000i2−i2i2−i2i2−i2i2−i200000000000000−i2i2−i2i2
χ402-222-22-2-22-22-2-20002-20000200000-22-220000−i2i2−i2i2−i2i2−i2i200000000000000i2−i2i2−i2
χ412-222-22-2-2-22-22-2000-2200002000002-2-220000i2−i2i2−i2−i2i2−i2i200000000000000i2−i2−i2i2
χ422-222-22-2-2-22-22-2000-2200002000002-2-220000−i2i2−i2i2i2−i2i2−i200000000000000−i2i2i2−i2
χ432-222-22-2-2-22-22-2000-220000200000-222-20000i2−i2i2−i2−i2i2−i2i200000000000000−i2i2i2−i2
χ442-222-22-2-2-22-22-2000-220000200000-222-20000−i2i2−i2i2i2−i2i2−i200000000000000i2−i2−i2i2
χ4544-444-4-4-444-4-40-4440000000-400000000000000000000000000000000000000
χ4644-444-4-4-4-4-44404-440000000-400000000000000000000000000000000000000
χ4744-4-4-444-40000000000004-40000000000004i−4i00000000000000000000000000
χ4844-4-4-444-40000000000004-4000000000000−4i4i00000000000000000000000000
χ4944-4-4-444-4000000000000-4400000000004i−4i0000000000000000000000000000
χ5044-4-4-444-4000000000000-440000000000−4i4i0000000000000000000000000000
χ514-444-44-4-44-44-44000-440000-4000000000000000000000000000000000000000
χ524-444-44-4-4-44-4440004-40000-4000000000000000000000000000000000000000
χ534-44-44-44-400000000004i−4i0000000000000000000000002-22i−2i00000000000000
χ544-44-44-44-400000000004i−4i000000000000000000000000-22−2i2i00000000000000
χ554-44-44-44-40000000000−4i4i0000000000000000000000002-2−2i2i00000000000000
χ564-44-44-44-40000000000−4i4i000000000000000000000000-222i−2i00000000000000
χ574-4-44-4-4444-4-440000000000000000000000002-2-222-2-22000000000000000000
χ584-4-44-4-4444-4-44000000000000000000000000-222-2-222-2000000000000000000
χ594-4-44-4-444-444-40000000000000000000000002-2-22-222-2000000000000000000
χ604-4-44-4-444-444-4000000000000000000000000-222-22-2-22000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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