Finite Group Databasebeta

← Group #394549

Character table — Group #394549

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222224444444422444422224444444444444444444488888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111-1-11-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-11111
χ91111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ121111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-11-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-111-111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-111-1-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-1-1111-1-1
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000002-20002-200000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000-22000-2200000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-2000-2200000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-220002-200000
χ2122222222-2-22222-2-2222-2-2-2-22-2-222-2-22222-2-2-2-2000000000000000000000000000000000000
χ2222222222-2-22222-2-2222-2-2-2-22-2-222-2-2-2-2-2-22222000000000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-22222-2-2-2-2-22200000000000000000000000000000000002-2200-20000
χ2422222222-2-22222-2-2-2-2-22222-2-2-2-2-2220000000000000000000000000000000000-22-20020000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-2-2222-2-22222-2-2-2-222000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-2-2222-2-222-2-22222-2-2000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-22222-2-200000000000000000000000000000000002-2-20020000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-22222-2-20000000000000000000000000000000000-22200-20000
χ2922-2-2-222-22222-2-2-2-222-2-2-222-22-22-22-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ3022-2-2-222-22222-2-2-2-222-2-2-222-22-22-22-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ3122-2-2-222-22222-2-2-2-2-2-2222-2-222-2-22-2200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ3222-2-2-222-22222-2-2-2-2-2-2222-2-222-2-22-220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ3322-2-2-222-222-2-222-2-222-2-2-222-2-22-22-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ3422-2-2-222-222-2-222-2-222-2-2-222-2-22-22-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ3522-2-2-222-222-2-222-2-2-2-2222-2-22-222-22-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ3622-2-2-222-222-2-222-2-2-2-2222-2-22-222-22-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ3722-2-2-222-2-2-222-2-22222-222-2-2-2-222-2-220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ3822-2-2-222-2-2-222-2-22222-222-2-2-2-222-2-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ3922-2-2-222-2-2-222-2-222-2-22-2-2222-22-222-200000000000000000000000000000000000000002-22-2
χ4022-2-2-222-2-2-222-2-222-2-22-2-2222-22-222-20000000000000000000000000000000000000000-22-22
χ4122-2-2-222-2-2-2-2-2222222-222-2-2-22-2-222-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ4222-2-2-222-2-2-2-2-2222222-222-2-2-22-2-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ4322-2-2-222-2-2-2-2-22222-2-22-2-22222-22-2-2200000000000000000000000000000000000000002-2-22
χ4422-2-2-222-2-2-2-2-22222-2-22-2-22222-22-2-220000000000000000000000000000000000000000-222-2
χ452-222-2-22-22-200002-22-222-22-2-20000002-2002-20000002i−2i2i−2i0000000000002i−2i2i−2i000000000000
χ462-222-2-22-22-200002-22-222-22-2-20000002-2002-2000000−2i2i−2i2i000000000000−2i2i−2i2i000000000000
χ472-222-2-22-22-200002-22-222-22-2-2000000-2200-220000002i−2i2i−2i000000000000−2i2i−2i2i000000000000
χ482-222-2-22-22-200002-22-222-22-2-2000000-2200-22000000−2i2i−2i2i0000000000002i−2i2i−2i000000000000
χ492-222-2-22-2-220000-222-22-22-22-20000002-200-22002i−2i2i−2i0000000000002i−2i2i−2i0000000000000000
χ502-222-2-22-2-220000-222-22-22-22-20000002-200-2200−2i2i−2i2i000000000000−2i2i−2i2i0000000000000000
χ512-222-2-22-2-220000-222-22-22-22-2000000-22002-2002i−2i2i−2i000000000000−2i2i−2i2i0000000000000000
χ522-222-2-22-2-220000-222-22-22-22-2000000-22002-200−2i2i−2i2i0000000000002i−2i2i−2i0000000000000000
χ532-2-2-22-2222-20000-222-2-2-222-22000000002-2002-200002-2-22000000002-2-220000000000000000
χ542-2-2-22-2222-20000-222-2-2-222-22000000002-2002-20000-222-200000000-222-20000000000000000
χ552-2-2-22-2222-20000-222-2-2-222-2200000000-2200-2200002-2-2200000000-222-20000000000000000
χ562-2-2-22-2222-20000-222-2-2-222-2200000000-2200-220000-222-2000000002-2-220000000000000000
χ572-2-2-22-222-2200002-22-2-22-2-222000000002-200-222-2-2200000000000000002-2-22000000000000
χ582-2-2-22-222-2200002-22-2-22-2-222000000002-200-22-222-20000000000000000-222-2000000000000
χ592-2-2-22-222-2200002-22-2-22-2-22200000000-22002-22-2-220000000000000000-222-2000000000000
χ602-2-2-22-222-2200002-22-2-22-2-22200000000-22002-2-222-200000000000000002-2-22000000000000
χ614-444-4-44-44-400004-4-44-4-44-44400000000000000000000000000000000000000000000000000
χ624-444-4-44-4-440000-44-44-44-44-4400000000000000000000000000000000000000000000000000
χ634-44-444-4-4004-44-4000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ644-44-444-4-4004-44-400000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ654-44-444-4-400-44-44000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ664-44-444-4-400-44-4400000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ674-4-44-44-44004-4-44000000000000000000000000000000002-2-222-2-2200000000000000000000
χ684-4-44-44-44004-4-4400000000000000000000000000000000-222-2-222-200000000000000000000
χ694-4-44-44-4400-444-4000000000000000000000000000000002-2-22-222-200000000000000000000
χ704-4-44-44-4400-444-400000000000000000000000000000000-222-22-2-2200000000000000000000
χ714-4-4-44-4444-40000-44-4444-4-44-400000000000000000000000000000000000000000000000000
χ724-4-4-44-444-4400004-4-444-444-4-400000000000000000000000000000000000000000000000000
χ73888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ7488-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000

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