Finite Group Databasebeta

← Group #398610

Character table — Group #398610

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422224444444444448888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-11-1
χ91111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-11-11
χ101111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-11-1
χ111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1111-11-1
χ121111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-11-11
χ131111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ141111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ151111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ161111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1
χ17222222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-2-2-222-2-2222222-2-222-2-2-2-2000000000000000000000000000000000000002-2020-2
χ2222222222-2-2-2-222-2-2222222-2-222-2-2-2-200000000000000000000000000000000000000-220-202
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000000000002-20-202
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000000000-22020-2
χ2522222222-2-2-2-2-2-2222222-2-222-2-222-2-20000000000000000000000000000000000002-20020-20
χ2622222222-2-2-2-2-2-2222222-2-222-2-222-2-2000000000000000000000000000000000000-2200-2020
χ2722222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2220000000000000000000000000000000000002-200-2020
χ2822222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-222000000000000000000000000000000000000-220020-20
χ292222-2-2-2-2-2-2222-22-200002-22-20000002-22-200000000000000002i2i−2i−2i00002i2i−2i−2i000000000000
χ302222-2-2-2-2-2-2222-22-200002-22-20000002-22-20000000000000000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ312222-2-2-2-2-2-2222-22-200002-22-2000000-22-2200000000000000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ322222-2-2-2-2-2-2222-22-200002-22-2000000-22-220000000000000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ332222-2-2-2-2-2-222-22-220000-22-220000002-2-220000000000002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ342222-2-2-2-2-2-222-22-220000-22-220000002-2-22000000000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ352222-2-2-2-2-2-222-22-220000-22-22000000-222-20000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ362222-2-2-2-2-2-222-22-220000-22-22000000-222-2000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ372-22-222-2-22-22-22-22-22i2i−2i−2i-22-222i−2i2i−2i2i−2i00000000000000002i−2i2i−2i2-22-200000000000000000000
χ382-22-222-2-22-22-22-22-22i2i−2i−2i-22-222i−2i2i−2i2i−2i0000000000000000−2i2i−2i2i-22-2200000000000000000000
χ392-22-222-2-22-22-22-22-2−2i−2i2i2i-22-22−2i2i−2i2i−2i2i00000000000000002i−2i2i−2i-22-2200000000000000000000
χ402-22-222-2-22-22-22-22-2−2i−2i2i2i-22-22−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i2-22-200000000000000000000
χ412-22-222-2-22-22-2-22-222i2i−2i−2i2-22-2−2i2i−2i2i2i−2i0000000000000000000000002-22-22i−2i2i−2i000000000000
χ422-22-222-2-22-22-2-22-222i2i−2i−2i2-22-2−2i2i−2i2i2i−2i000000000000000000000000-22-22−2i2i−2i2i000000000000
χ432-22-222-2-22-22-2-22-22−2i−2i2i2i2-22-22i−2i2i−2i−2i2i0000000000000000000000002-22-2−2i2i−2i2i000000000000
χ442-22-222-2-22-22-2-22-22−2i−2i2i2i2-22-22i−2i2i−2i−2i2i000000000000000000000000-22-222i−2i2i−2i000000000000
χ452-22-222-2-2-22-222-2-222i2i−2i−2i-222-22i−2i−2i2i−2i2i000000000000000000000000000000002-22i−2i00000000
χ462-22-222-2-2-22-222-2-222i2i−2i−2i-222-22i−2i−2i2i−2i2i00000000000000000000000000000000-22−2i2i00000000
χ472-22-222-2-2-22-222-2-22−2i−2i2i2i-222-2−2i2i2i−2i2i−2i000000000000000000000000000000002-2−2i2i00000000
χ482-22-222-2-2-22-222-2-22−2i−2i2i2i-222-2−2i2i2i−2i2i−2i00000000000000000000000000000000-222i−2i00000000
χ492-22-222-2-2-22-22-222-22i2i−2i−2i2-2-22−2i2i2i−2i−2i2i0000000022-2-22i2i−2i−2i0000000000000000000000000000
χ502-22-222-2-2-22-22-222-22i2i−2i−2i2-2-22−2i2i2i−2i−2i2i00000000-2-222−2i−2i2i2i0000000000000000000000000000
χ512-22-222-2-2-22-22-222-2−2i−2i2i2i2-2-222i−2i−2i2i2i−2i0000000022-2-2−2i−2i2i2i0000000000000000000000000000
χ522-22-222-2-2-22-22-222-2−2i−2i2i2i2-2-222i−2i−2i2i2i−2i00000000-2-2222i2i−2i−2i0000000000000000000000000000
χ532-22-2-2-222-222-222220000-2-2-2-200000000002-22-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ542-22-2-2-222-222-222220000-2-2-2-200000000002-22-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ552-22-2-2-222-222-222220000-2-2-2-20000000000-22-220000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ562-22-2-2-222-222-222220000-2-2-2-20000000000-22-22000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ572-22-2-2-222-222-2-2-2-2-20000222200000000002-2-22000000002-2-2200000000-222-2000000000000
χ582-22-2-2-222-222-2-2-2-2-20000222200000000002-2-2200000000-222-2000000002-2-22000000000000
χ592-22-2-2-222-222-2-2-2-2-2000022220000000000-222-2000000002-2-22000000002-2-22000000000000
χ602-22-2-2-222-222-2-2-2-2-2000022220000000000-222-200000000-222-200000000-222-2000000000000
χ614444-4-4-4-444-4-44-4-4400004-4-4400000000000000000000000000000000000000000000000000
χ624444-4-4-4-444-4-4-444-40000-444-400000000000000000000000000000000000000000000000000
χ6344-4-44-44-4000000004i−4i4i−4i0000000000000000002-22-22i−2i2i−2i0000000000000000000000000000
χ6444-4-44-44-4000000004i−4i4i−4i000000000000000000-22-22−2i2i−2i2i0000000000000000000000000000
χ6544-4-44-44-400000000−4i4i−4i4i0000000000000000002-22-2−2i2i−2i2i0000000000000000000000000000
χ6644-4-44-44-400000000−4i4i−4i4i000000000000000000-22-222i−2i2i−2i0000000000000000000000000000
χ674-44-4-4-4444-4-4444-4-40000-4-44400000000000000000000000000000000000000000000000000
χ684-44-4-4-4444-4-44-4-444000044-4-400000000000000000000000000000000000000000000000000
χ694-4-444-4-44000000004-4-440000000000000000002-2-222-2-220000000000000000000000000000
χ704-4-444-4-44000000004-4-44000000000000000000-222-2-222-20000000000000000000000000000
χ714-4-444-4-4400000000-444-40000000000000000002-2-22-222-20000000000000000000000000000
χ724-4-444-4-4400000000-444-4000000000000000000-222-22-2-220000000000000000000000000000
χ7388-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000

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