Finite Group Databasebeta

← Group #417133

Character table — Group #417133

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888224444444444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ141111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ151111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ161111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ17222222222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-2-2-222-2-2222222-2-2-2-222-2-200000000000000000000000000000000000000002-22-2
χ2222222222-2-2-2-222-2-2222222-2-2-2-222-2-20000000000000000000000000000000000000000-22-22
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-222-2-22200000000000000000000000000000000000000002-2-22
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-222-2-2220000000000000000000000000000000000000000-222-2
χ2522222222-2-2-2-2-2-2222222-2-222-2-2-2-2220000000000000000000000000000000000002-22-20000
χ2622222222-2-2-2-2-2-2222222-2-222-2-2-2-222000000000000000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-20000000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000-222-20000
χ2922-22-22-2-22-2-222-22-200002-22-200000000002-22-20000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3022-22-22-2-22-2-222-22-200002-22-200000000002-22-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3122-22-22-2-22-2-222-22-200002-22-20000000000-22-220000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ3222-22-22-2-22-2-222-22-200002-22-20000000000-22-22000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ3322-22-22-2-22-2-22-22-220000-22-2200000000002-2-22000000002i2i−2i−2i000000002i2i−2i−2i000000000000
χ3422-22-22-2-22-2-22-22-220000-22-2200000000002-2-2200000000−2i−2i2i2i00000000−2i−2i2i2i000000000000
χ3522-22-22-2-22-2-22-22-220000-22-220000000000-222-2000000002i2i−2i−2i00000000−2i−2i2i2i000000000000
χ3622-22-22-2-22-2-22-22-220000-22-220000000000-222-200000000−2i−2i2i2i000000002i2i−2i−2i000000000000
χ372-22-222-2-2-22-222-2-220000-222-20000002-22-20000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ382-22-222-2-2-22-222-2-220000-222-20000002-22-2000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ392-22-222-2-2-22-222-2-220000-222-2000000-22-220000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ402-22-222-2-2-22-222-2-220000-222-2000000-22-22000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ412-22-222-2-2-22-22-222-200002-2-220000002-2-2200000000000000002i−2i2i−2i00002i−2i2i−2i000000000000
χ422-22-222-2-2-22-22-222-200002-2-220000002-2-220000000000000000−2i2i−2i2i0000−2i2i−2i2i000000000000
χ432-22-222-2-2-22-22-222-200002-2-22000000-222-200000000000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ442-22-222-2-2-22-22-222-200002-2-22000000-222-20000000000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ452-2-2-2-222222-2-2222222-2-2-2-2-2-22-22-22-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ462-2-2-2-222222-2-2222222-2-2-2-2-2-22-22-22-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ472-2-2-2-222222-2-22222-2-222-2-2-2-2-22-22-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ482-2-2-2-222222-2-22222-2-222-2-2-2-2-22-22-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ492-2-2-2-222222-2-2-2-2-2-222-2-222222-2-22-22000000000000000000000000000000002-22-200000000
χ502-2-2-2-222222-2-2-2-2-2-222-2-222222-2-22-2200000000000000000000000000000000-22-2200000000
χ512-2-2-2-222222-2-2-2-2-2-2-2-2222222-222-22-2000000000000000000000000000000002-2-2200000000
χ522-2-2-2-222222-2-2-2-2-2-2-2-2222222-222-22-200000000000000000000000000000000-222-200000000
χ532-2-2-2-2222-2-22222-2-222-2-2-2-222-222-2-220000000000000000000000002-2-222-2-22000000000000
χ542-2-2-2-2222-2-22222-2-222-2-2-2-222-222-2-22000000000000000000000000-222-2-222-2000000000000
χ552-2-2-2-2222-2-22222-2-2-2-222-2-2222-2-222-20000000000000000000000002-2-22-222-2000000000000
χ562-2-2-2-2222-2-22222-2-2-2-222-2-2222-2-222-2000000000000000000000000-222-22-2-22000000000000
χ572-2-2-2-2222-2-222-2-22222-2-222-2-2-22-222-200000000000000002-2-22-222-200000000000000000000
χ582-2-2-2-2222-2-222-2-22222-2-222-2-2-22-222-20000000000000000-222-22-2-2200000000000000000000
χ592-2-2-2-2222-2-222-2-222-2-22222-2-22-22-2-2200000000000000002-2-222-2-2200000000000000000000
χ602-2-2-2-2222-2-222-2-222-2-22222-2-22-22-2-220000000000000000-222-2-222-200000000000000000000
χ6144-44-44-4-4-444-44-4-4400004-4-4400000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-444-4-444-40000-444-400000000000000000000000000000000000000000000000000
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
χ674-444-4-44-4000000004i−4i−4i4i0000000000000000002i−2i−2i2i-222-20000000000000000000000000000
χ684-444-4-44-4000000004i−4i−4i4i000000000000000000−2i2i2i−2i2-2-220000000000000000000000000000
χ694-444-4-44-400000000−4i4i4i−4i0000000000000000002i−2i−2i2i2-2-220000000000000000000000000000
χ704-444-4-44-400000000−4i4i4i−4i000000000000000000−2i2i2i−2i-222-20000000000000000000000000000
χ714-44-444-4-44-44-44-44-40000-44-4400000000000000000000000000000000000000000000000000
χ724-44-444-4-44-44-4-44-4400004-44-400000000000000000000000000000000000000000000000000
χ73888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000

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