Finite Group Databasebeta

← Group #252473

Character table — Group #252473

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111222244444488888888888161616161616161616161616161616161616161616161616
order12222222222244444422444444444222244444444444488888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ5111111111111111111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111-1-111-1-111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111-1-111-1-1-1-11-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1
χ8111111111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111
χ91111111111111-1-111111-1-1-1-111-11111-1-1-1-11-11-11-111-1-111-1-111-1-1
χ101111111111111-1-111111-1-1-1-111-111-1-111-1-11-11-11-1-1-111-1-111-1-111
χ111111111111111-1-111111-1-1-1-1-1-1-1-1-111-1-111-111-1-1111-1-1-1-111-1-111
χ121111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-11-1-11111-1-111-1-1
χ131111111111111-1-1111-1-1-1-11111-11111-1-1-1-1-11-11-11-1-111-1-11111-1-1
χ141111111111111-1-1111-1-1-1-11111-111-1-111-1-1-11-11-1111-1-111-1-1-1-111
χ151111111111111-1-1111-1-1-1-111-1-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-111
χ161111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-111111-1-111-111-1-1-1-11111-1-1
χ17222222222222-222-2-2-222-2-2220020000000000-2-200000000000000
χ18222222222222-222-2-2-2-2-2-2-2-2-200200000000002200000000000000
χ19222222222222-2-2-2-2-2-22222-2-200-20000000000-2200000000000000
χ20222222222222-2-2-2-2-2-2-2-2222200-200000000002-200000000000000
χ2122222222-2-2-2-2222-2-22002-20022-2-2-200002-2000000000000000000
χ2222222222-2-2-2-2222-2-22002-200-2-2-2220000-22000000000000000000
χ2322222222-2-2-2-22-2-2-2-2200-2200222-2-20000-22000000000000000000
χ2422222222-2-2-2-22-2-2-2-2200-2200-2-222200002-2000000000000000000
χ2522222222-2-2-2-2-22222-200-220000-2000000002200-2-2000000000000
χ2622222222-2-2-2-2-22222-200-220000-200000000-2-20022000000000000
χ2722222222-2-2-2-2-2-2-222-2002-200002000000002-200-22000000000000
χ2822222222-2-2-2-2-2-2-222-2002-20000200000000-22002-2000000000000
χ2922-22-2-22-22-22-22002-2-20000002i−2i02i−2i002-20000000000000000002i−2i
χ3022-22-2-22-22-22-22002-2-20000002i−2i02i−2i00-22000000000000000000−2i2i
χ3122-22-2-22-22-22-22002-2-2000000−2i2i0−2i2i002-2000000000000000000−2i2i
χ3222-22-2-22-22-22-22002-2-2000000−2i2i0−2i2i00-220000000000000000002i−2i
χ3322-22-2-22-2-22-22200-22-20000002i−2i0−2i2i2-20000000000000000002i−2i00
χ3422-22-2-22-2-22-22200-22-20000002i−2i0−2i2i-22000000000000000000−2i2i00
χ3522-22-2-22-2-22-22200-22-2000000−2i2i02i−2i2-2000000000000000000−2i2i00
χ3622-22-2-22-2-22-22200-22-2000000−2i2i02i−2i-220000000000000000002i−2i00
χ37444-44-4-4-44-4-440000000000000000000000000000000002i2−2i2000000
χ38444-44-4-4-44-4-44000000000000000000000000000000000−2i22i2000000
χ39444-44-4-4-4-444-4000000000000000000000000000000000002i2−2i20000
χ40444-44-4-4-4-444-400000000000000000000000000000000000−2i22i20000
χ4144-44-4-44-44-44-4-400-44400000000000000000000000000000000000
χ4244-44-4-44-4-44-44-4004-4400000000000000000000000000000000000
χ4344-4-4-44-4444-4-400000000004i−4i00000000000000000000000000000
χ4444-4-4-44-4444-4-40000000000−4i4i00000000000000000000000000000
χ4544-4-4-44-44-4-4440000004-4000000000000000000000000000000000
χ4644-4-4-44-44-4-444000000-44000000000000000000000000000000000
χ474-4-4-44-444000004-4000000000000000000000000002-22-200000000
χ484-4-4-44-444000004-400000000000000000000000000-22-2200000000
χ494-4-4-44-44400000-44000000000000000000000000002-2-2200000000
χ504-4-4-44-44400000-4400000000000000000000000000-222-200000000
χ518-888-8-8-88000000000000000000000000000000000000000000000
χ528-88-8-888-8000000000000000000000000000000000000000000000
χ538-8-8888-8-8000000000000000000000000000000000000000000000

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