Finite Group Databasebeta

← Group #403330

Character table — Group #403330

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222224444444422444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ121111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000022-2-222-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-222-2-22200000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-2-2-22200000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000-2-22222-2-200000000000000000000
χ2122222222-2-22222-2-222-2-222-2-2-2-222-2-2000022220000-2-2-2-20000000000000000000000000000
χ2222222222-2-22222-2-222-2-222-2-2-2-222-2-20000-2-2-2-2000022220000000000000000000000000000
χ2322222222-2-22222-2-2-2-222-2-222-2-2-2-22222220000-2-2-2-200000000000000000000000000000000
χ2422222222-2-22222-2-2-2-222-2-222-2-2-2-222-2-2-2-20000222200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222000022-2-20000-2-2220000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000-2-222000022-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-222-2-20000-2-22200000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-222000022-2-200000000000000000000000000000000
χ2922-2-222-2-22222-2-2-2-22222-2-2-2-22-22-22-2000000000000000000000000000000002-22-200000000
χ3022-2-222-2-22222-2-2-2-22222-2-2-2-22-22-22-200000000000000000000000000000000-22-2200000000
χ3122-2-222-2-22222-2-2-2-2-2-2-2-222222-2-22-220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ3222-2-222-2-22222-2-2-2-2-2-2-2-222222-2-22-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ3322-2-222-2-222-2-222-2-22222-2-2-2-2-22-22-22000000000000000000000000000000002-2-2200000000
χ3422-2-222-2-222-2-222-2-22222-2-2-2-2-22-22-2200000000000000000000000000000000-222-200000000
χ3522-2-222-2-222-2-222-2-2-2-2-2-22222-222-22-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ3622-2-222-2-222-2-222-2-2-2-2-2-22222-222-22-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ3722-2-222-2-2-2-222-2-22222-2-2-2-222-222-2-220000000000000000000000000000000000002i−2i2i−2i0000
χ3822-2-222-2-2-2-222-2-22222-2-2-2-222-222-2-22000000000000000000000000000000000000−2i2i−2i2i0000
χ3922-2-222-2-2-2-222-2-222-2-22222-2-2-22-222-200000000000000000000000000000000000000002i−2i2i−2i
χ4022-2-222-2-2-2-222-2-222-2-22222-2-2-22-222-20000000000000000000000000000000000000000−2i2i−2i2i
χ4122-2-222-2-2-2-2-2-2222222-2-2-2-2222-2-222-20000000000000000000000000000000000002i−2i−2i2i0000
χ4222-2-222-2-2-2-2-2-2222222-2-2-2-2222-2-222-2000000000000000000000000000000000000−2i2i2i−2i0000
χ4322-2-222-2-2-2-2-2-22222-2-22222-2-22-22-2-2200000000000000000000000000000000000000002i−2i−2i2i
χ4422-2-222-2-2-2-2-2-22222-2-22222-2-22-22-2-220000000000000000000000000000000000000000−2i2i2i−2i
χ452-2-2-2-22222-200002-22-22-22-22-2000000002-2002-2002-2002-22-22-2000000000000000000000000
χ462-2-2-2-22222-200002-22-22-22-22-2000000002-200-22002-200-22-22-22000000000000000000000000
χ472-2-2-2-22222-200002-22-22-22-22-200000000-22002-200-22002-2-22-22000000000000000000000000
χ482-2-2-2-22222-200002-22-22-22-22-200000000-2200-2200-2200-222-22-2000000000000000000000000
χ492-2-2-2-22222-200002-2-22-22-22-220000002-2002-2002-2002-2002-2-22000000000000000000000000
χ502-2-2-2-22222-200002-2-22-22-22-220000002-200-22002-200-2200-222-2000000000000000000000000
χ512-2-2-2-22222-200002-2-22-22-22-22000000-22002-200-22002-200-222-2000000000000000000000000
χ522-2-2-2-22222-200002-2-22-22-22-22000000-2200-2200-2200-22002-2-22000000000000000000000000
χ532-2-2-2-2222-220000-222-2-222-2-220000002-200002-2-220000-2200002-22-200000000000000000000
χ542-2-2-2-2222-220000-222-2-222-2-220000002-20000-22-2200002-20000-22-2200000000000000000000
χ552-2-2-2-2222-220000-222-2-222-2-22000000-2200002-22-20000-220000-22-2200000000000000000000
χ562-2-2-2-2222-220000-222-2-222-2-22000000-220000-222-200002-200002-22-200000000000000000000
χ572-2-2-2-2222-220000-22-222-2-222-2000000002-22-20000-22-220000002-2-2200000000000000000000
χ582-2-2-2-2222-220000-22-222-2-222-2000000002-2-220000-222-2000000-222-200000000000000000000
χ592-2-2-2-2222-220000-22-222-2-222-200000000-222-200002-2-22000000-222-200000000000000000000
χ602-2-2-2-2222-220000-22-222-2-222-200000000-22-2200002-22-20000002-2-2200000000000000000000
χ61444-4-4-44-4004-44-400000000000000000000000000000000000000002-22-22-22-2000000000000
χ62444-4-4-44-4004-44-40000000000000000000000000000000000000000-22-22-22-22000000000000
χ63444-4-4-44-400-44-4400000000000000000000000000000000000000002-22-2-22-22000000000000
χ64444-4-4-44-400-44-440000000000000000000000000000000000000000-22-222-22-2000000000000
χ6544-44-4-4-44004-4-4400000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ6644-44-4-4-44004-4-440000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ6744-44-4-4-4400-444-400000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ6844-44-4-4-4400-444-40000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ694-444-44-4-44-40000-444-44-4-44-4400000000000000000000000000000000000000000000000000
χ704-444-44-4-44-40000-44-44-444-44-400000000000000000000000000000000000000000000000000
χ714-444-44-4-4-4400004-44-4-44-444-400000000000000000000000000000000000000000000000000
χ724-444-44-4-4-4400004-4-444-44-4-4400000000000000000000000000000000000000000000000000
χ738-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000

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