Finite Group Databasebeta

← Group #415598

Character table — Group #415598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ141111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ151111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ161111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ17222222222222-2-2-2-22222-2-2-2-2-2-2-2-222000022-2-20000000022-2-2000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2-2-2-2-2220000-2-22200000000-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000022-2-200000000-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000-2-2220000000022-2-2000000000000000000000000
χ2122222222-2-2-2-222-2-2222222-2-222-2-2-2-2002200000000-2-2-2-20000002200000000000000000000
χ2222222222-2-2-2-222-2-2222222-2-222-2-2-2-200-2-2000000002222000000-2-200000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-2-2-22222002200000000-2-222000000-2-200000000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-2-2-2222200-2-20000000022-2-20000002200000000000000000000
χ2522222222-2-2-2-2-2-2222222-2-222-2-222-2-222000000-2-2-2-200000000220000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-222-2-222-2-2-2-2000000222200000000-2-20000000000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-22222000000-2-22200000000-2-20000000000000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-222-2-200000022-2-200000000220000000000000000000000
χ2922-222-2-2-222-2-222220000-2-2-2-20000002-22-22-22-22-2002-2000000000000000000000000000000
χ3022-222-2-2-222-2-222220000-2-2-2-20000002-2-22-22-222-200-22000000000000000000000000000000
χ3122-222-2-2-222-2-222220000-2-2-2-2000000-222-2-22-22-22002-2000000000000000000000000000000
χ3222-222-2-2-222-2-222220000-2-2-2-2000000-22-222-22-2-2200-22000000000000000000000000000000
χ3322-222-2-2-222-2-2-2-2-2-20000222200000000002-2-22002i−2i002i−2i00002i−2i2i−2i00000000000000000000
χ3422-222-2-2-222-2-2-2-2-2-20000222200000000002-2-2200−2i2i00−2i2i0000−2i2i−2i2i00000000000000000000
χ3522-222-2-2-222-2-2-2-2-2-2000022220000000000-222-2002i−2i00−2i2i00002i−2i−2i2i00000000000000000000
χ3622-222-2-2-222-2-2-2-2-2-2000022220000000000-222-200−2i2i002i−2i0000−2i2i2i−2i00000000000000000000
χ3722-222-2-2-2-2-22222-2-20000-2-222000000002-20000002i−2i-22002i−2i2i−2i−2i2i0000000000000000000000
χ3822-222-2-2-2-2-22222-2-20000-2-222000000002-2000000−2i2i-2200−2i2i−2i2i2i−2i0000000000000000000000
χ3922-222-2-2-2-2-22222-2-20000-2-22200000000-220000002i−2i2-200−2i2i−2i2i−2i2i0000000000000000000000
χ4022-222-2-2-2-2-22222-2-20000-2-22200000000-22000000−2i2i2-2002i−2i2i−2i2i−2i0000000000000000000000
χ4122-222-2-2-2-2-222-2-222000022-2-20000002-2000000-2200002i−2i2i−2i−2i2i00−2i2i00000000000000000000
χ4222-222-2-2-2-2-222-2-222000022-2-20000002-2000000-220000−2i2i−2i2i2i−2i002i−2i00000000000000000000
χ4322-222-2-2-2-2-222-2-222000022-2-2000000-220000002-200002i−2i−2i2i2i−2i00−2i2i00000000000000000000
χ4422-222-2-2-2-2-222-2-222000022-2-2000000-220000002-20000−2i2i2i−2i−2i2i002i−2i00000000000000000000
χ452-22-22-22-22-22-22-22-22i2i−2i−2i2-22-22i−2i2i−2i2i−2i00000000000000000000000000000000000000002-22i−2i
χ462-22-22-22-22-22-22-22-22i2i−2i−2i2-22-22i−2i2i−2i2i−2i0000000000000000000000000000000000000000-22−2i2i
χ472-22-22-22-22-22-22-22-2−2i−2i2i2i2-22-2−2i2i−2i2i−2i2i00000000000000000000000000000000000000002-2−2i2i
χ482-22-22-22-22-22-22-22-2−2i−2i2i2i2-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000000-222i−2i
χ492-22-22-22-22-22-2-22-222i2i−2i−2i-22-22−2i2i−2i2i2i−2i0000000000000000000000000000000000002-22i−2i0000
χ502-22-22-22-22-22-2-22-222i2i−2i−2i-22-22−2i2i−2i2i2i−2i000000000000000000000000000000000000-22−2i2i0000
χ512-22-22-22-22-22-2-22-22−2i−2i2i2i-22-222i−2i2i−2i−2i2i0000000000000000000000000000000000002-2−2i2i0000
χ522-22-22-22-22-22-2-22-22−2i−2i2i2i-22-222i−2i2i−2i−2i2i000000000000000000000000000000000000-222i−2i0000
χ532-22-22-22-2-22-222-2-222i2i−2i−2i2-2-222i−2i−2i2i−2i2i0000000000000000000000002i2i−2i−2i22-2-2000000000000
χ542-22-22-22-2-22-222-2-222i2i−2i−2i2-2-222i−2i−2i2i−2i2i000000000000000000000000−2i−2i2i2i-2-222000000000000
χ552-22-22-22-2-22-222-2-22−2i−2i2i2i2-2-22−2i2i2i−2i2i−2i0000000000000000000000002i2i−2i−2i-2-222000000000000
χ562-22-22-22-2-22-222-2-22−2i−2i2i2i2-2-22−2i2i2i−2i2i−2i000000000000000000000000−2i−2i2i2i22-2-2000000000000
χ572-22-22-22-2-22-22-222-22i2i−2i−2i-222-2−2i2i2i−2i−2i2i000000000000000000000000000000002-22i−2i00000000
χ582-22-22-22-2-22-22-222-22i2i−2i−2i-222-2−2i2i2i−2i−2i2i00000000000000000000000000000000-22−2i2i00000000
χ592-22-22-22-2-22-22-222-2−2i−2i2i2i-222-22i−2i−2i2i2i−2i000000000000000000000000000000002-2−2i2i00000000
χ602-22-22-22-2-22-22-222-2−2i−2i2i2i-222-22i−2i−2i2i2i−2i00000000000000000000000000000000-222i−2i00000000
χ6144-4-4-444-4000000004i−4i4i−4i00000000000000000000000000000000002i−2i2i−2i2-22-2000000000000
χ6244-4-4-444-4000000004i−4i4i−4i0000000000000000000000000000000000−2i2i−2i2i-22-22000000000000
χ6344-4-4-444-400000000−4i4i−4i4i00000000000000000000000000000000002i−2i2i−2i-22-22000000000000
χ6444-4-4-444-400000000−4i4i−4i4i0000000000000000000000000000000000−2i2i−2i2i2-22-2000000000000
χ654-4-44-4-444000000004-4-4400000000000000000000000000000000002-2-222-2-22000000000000
χ664-4-44-4-444000000004-4-440000000000000000000000000000000000-222-2-222-2000000000000
χ674-4-44-4-44400000000-444-400000000000000000000000000000000002-2-22-222-2000000000000
χ684-4-44-4-44400000000-444-40000000000000000000000000000000000-222-22-2-22000000000000
χ694-4-4-444-444-4-444-44-40000-44-4400000000000000000000000000000000000000000000000000
χ704-4-4-444-444-4-44-44-4400004-44-400000000000000000000000000000000000000000000000000
χ714-4-4-444-44-444-44-4-440000-444-400000000000000000000000000000000000000000000000000
χ724-4-4-444-44-444-4-444-400004-4-4400000000000000000000000000000000000000000000000000
χ73888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000

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