Finite Group Databasebeta

← Group #303301

Character table — Group #303301

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111222244444488888888888161616161616161616161616161616161616161616161616
order12222222222244444422224444444224444444444444488888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-111111-1-1-1-11-1111-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-111111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-111111-1-111-1-1-11-1111-1-111-1-1-1-1-1-1-1-11111
χ6111111111111111111-1-111111-1-111-1-1-11-1-1-11-1-1-1-111111111-1-1-1-1
χ7111111111111111111-1-1-1-1111-1-1-1-111-1-1-111-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ91111111111111-1-11111111-1-1-1-1-1111-11-1-111-11-1-1-111-1-111-1-111-1-1
χ101111111111111-1-11111111-1-1-1-1-1111-11-1-1-1-1-11-111-1-111-1-111-1-111
χ111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1111-1111-11-1-111-1-1-1-111-1-111
χ121111111111111-1-111111-1-1-1-1-1-1-1-1-1-1111-1-1-11-1111-1-11111-1-111-1-1
χ131111111111111-1-1111-1-111-1-1-11111-11-1-1111-1-11-1-1-1-111-1-11111-1-1
χ141111111111111-1-1111-1-111-1-1-11111-11-1-11-1-1-1-111111-1-111-1-1-1-111
χ151111111111111-1-1111-1-1-1-1-1-1-111-1-11-1-1111111-1-1-1-1-11111-1-1-1-111
χ161111111111111-1-1111-1-1-1-1-1-1-111-1-11-1-111-1-111-11111-1-1-1-11111-1-1
χ17222222222222-222-2-2-22200-2-22220000-20-20000000000000000000
χ18222222222222-222-2-2-2-2-200-2-22-2-200002020000000000000000000
χ19222222222222-2-2-2-2-2-2220022-2-2-20000-2020000000000000000000
χ20222222222222-2-2-2-2-2-2-2-20022-222000020-20000000000000000000
χ2122222222-2-2-2-2222-2-2200222-2-200-2-2000-200020000000000000000
χ2222222222-2-2-2-2222-2-2200-2-22-2-200220002000-20000000000000000
χ2322222222-2-2-2-22-2-2-2-220022-22200-2-20002000-20000000000000000
χ2422222222-2-2-2-22-2-2-2-2200-2-2-2220022000-200020000000000000000
χ2522222222-2-2-2-2-22222-20000-22-200002-2000000-2200000000000000
χ2622222222-2-2-2-2-22222-20000-22-20000-220000002-200000000000000
χ2722222222-2-2-2-2-2-2-222-200002-22000022000000-2-200000000000000
χ2822222222-2-2-2-2-2-2-222-200002-220000-2-20000002200000000000000
χ2922-2-22-22-22-22-22002-2-2002-2000002-2000000000000002i−2i002i−2i0000
χ3022-2-22-22-22-22-22002-2-2002-2000002-200000000000000−2i2i00−2i2i0000
χ3122-2-22-22-22-22-22002-2-200-2200000-22000000000000002i−2i00−2i2i0000
χ3222-2-22-22-22-22-22002-2-200-2200000-2200000000000000−2i2i002i−2i0000
χ3322-2-22-22-2-22-22200-22-2002-200000-220000000000002i−2i002i−2i000000
χ3422-2-22-22-2-22-22200-22-2002-200000-22000000000000−2i2i00−2i2i000000
χ3522-2-22-22-2-22-22200-22-200-22000002-20000000000002i−2i00−2i2i000000
χ3622-2-22-22-2-22-22200-22-200-22000002-2000000000000−2i2i002i−2i000000
χ3744-4-44-44-44-44-4-400-44400000000000000000000000000000000000
χ3844-4-44-44-4-44-44-4004-4400000000000000000000000000000000000
χ394-44-444-4-4000004i−4i00000000000000000002-20002i−2i000000000000
χ404-44-444-4-4000004i−4i0000000000000000000-22000−2i2i000000000000
χ414-44-444-4-400000−4i4i00000000000000000002-2000−2i2i000000000000
χ424-44-444-4-400000−4i4i0000000000000000000-220002i−2i000000000000
χ434-44-4-4-4444-4-440000004-4000000000000000000000000000000000
χ444-44-4-4-4444-4-44000000-44000000000000000000000000000000000
χ454-44-4-4-444-444-400000000000004-400000000000000000000000000
χ464-44-4-4-444-444-40000000000000-4400000000000000000000000000
χ474-4-44-444-444-4-40000000000000000000000000000000000000002i2−2i2
χ484-4-44-444-444-4-4000000000000000000000000000000000000000−2i22i2
χ494-4-44-444-4-4-444000000000000000000000000000000000000022−2200
χ504-4-44-444-4-4-4440000000000000000000000000000000000000−222200
χ518888-8-8-8-8000000000000000000000000000000000000000000000
χ5288-8-8-88-88000000000000000000000000000000000000000000000
χ538-8-888-8-88000000000000000000000000000000000000000000000

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