Finite Group Databasebeta

← Group #405221

Character table — Group #405221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222222244444444442222222222444444444444444444444444442444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-111-1-111-1-1
χ1011111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-111-1-111-1-111
χ1111111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-111-1-111
χ1211111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-111-1-1
χ1311111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1
χ1411111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-111-1-111-1-1-1-111
χ1511111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-1-11111-1-1-1-111
χ1611111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-111-1-1-1-11111-1-1
χ172222222222-222-2-2-2-2-2-2-2-2-222-2-2222-2000000002-20000000000000000000000000000000000002-22-2
χ182222222222-222-2-2-2-2-2-2-2-2-222-2-2222-2000000002-2000000000000000000000000000000000000-22-22
χ192222222222-2-2-222-2-2-2-2-2-2-2-2-22222-2200000000-220000000000000000000000000000000000002-2-22
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-22222-2200000000-22000000000000000000000000000000000000-222-2
χ2122222222-2-222222-2-2222-2-22222-2-2-2-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ2222222222-2-222222-2-2222-2-22222-2-2-2-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ2322222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-2-2-2220000000022000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-2-2-22200000000220000000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-222-2-222-2-2-22222-2-2-2-2-2200000000-2200000000000000000000000000002-22-200000000
χ2622222222-2-2-222-2-222-2-2-22222-2-2-2-2-2200000000-220000000000000000000000000000-22-2200000000
χ2722222222-2-2-2-2-22222-2-2-222-2-222-2-22-2000000002-200000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-22222-2-2-222-2-222-2-22-2000000002-20000000000000000000000000000-222-200000000
χ292222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ302222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ312222-2-2-2-2222-2-2-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ322222-2-2-2-2222-2-2-2-2222-2-2-2-22222-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ332222-2-2-2-222-222-2-2-2-2-22222-2-222-2-22-200000000-22000000000000000000000000000000002i−2i2i−2i0000
χ342222-2-2-2-222-222-2-2-2-2-22222-2-222-2-22-200000000-2200000000000000000000000000000000−2i2i−2i2i0000
χ352222-2-2-2-222-2-2-222-2-2-2222222-2-2-2-2-22000000002-2000000000000000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-222-2-2-222-2-2-2222222-2-2-2-2-22000000002-200000000000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-2-2-2-222222-2-22-2-222-2-2-2-222-2-200000000220000000022-2-222-2-2000000000000000000000000
χ382222-2-2-2-2-2-222222-2-22-2-222-2-2-2-222-2-2000000002200000000-2-222-2-222000000000000000000000000
χ392222-2-2-2-2-2-22-2-2-2-2-2-22-2-2222222222200000000-2-20000000022-2-2-2-222000000000000000000000000
χ402222-2-2-2-2-2-22-2-2-2-2-2-22-2-2222222222200000000-2-200000000-2-22222-2-2000000000000000000000000
χ412222-2-2-2-2-2-2-222-2-222-222-2-2-2-22222-22000000002-200000000000000000000000022-2-2000000000000
χ422222-2-2-2-2-2-2-222-2-222-222-2-2-2-22222-22000000002-2000000000000000000000000-2-222000000000000
χ432222-2-2-2-2-2-2-2-2-22222-222-2-222-2-2222-200000000-220000000000000000000000002-22-2000000000000
χ442222-2-2-2-2-2-2-2-2-22222-222-2-222-2-2222-200000000-22000000000000000000000000-22-22000000000000
χ452-2-2222-2-22-2200002-2-22-22-200002-200000022-2-200000022-2-200002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ462-2-2222-2-22-2200002-2-22-22-200002-200000022-2-200000022-2-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ472-2-2222-2-22-2200002-2-22-22-200002-2000000-2-222000000-2-22200002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ482-2-2222-2-22-2200002-2-22-22-200002-2000000-2-222000000-2-2220000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ492-2-2222-2-2-2220000-22-22-2-220000-220022-2-200000022-2-200002i−2i2i−2i00002i−2i−2i2i00000000000000000000
χ502-2-2222-2-2-2220000-22-22-2-220000-220022-2-200000022-2-20000−2i2i−2i2i0000−2i2i2i−2i00000000000000000000
χ512-2-2222-2-2-2220000-22-22-2-220000-2200-2-222000000-2-22200002i−2i2i−2i0000−2i2i2i−2i00000000000000000000
χ522-2-2222-2-2-2220000-22-22-2-220000-2200-2-222000000-2-2220000−2i2i−2i2i00002i−2i−2i2i00000000000000000000
χ532-2-22-2-2222-2200002-2-2-22-220000-2200000022-2-2000000-2-2222i−2i−2i2i000000002i−2i2i−2i0000000000000000
χ542-2-22-2-2222-2200002-2-2-22-220000-2200000022-2-2000000-2-222−2i2i2i−2i00000000−2i2i−2i2i0000000000000000
χ552-2-22-2-2222-2200002-2-2-22-220000-22000000-2-22200000022-2-22i−2i−2i2i00000000−2i2i−2i2i0000000000000000
χ562-2-22-2-2222-2200002-2-2-22-220000-22000000-2-22200000022-2-2−2i2i2i−2i000000002i−2i2i−2i0000000000000000
χ572-2-22-2-222-2220000-22-2-222-200002-20022-2-2000000-2-222000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ582-2-22-2-222-2220000-22-2-222-200002-20022-2-2000000-2-22200000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ592-2-22-2-222-2220000-22-2-222-200002-200-2-22200000022-2-2000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ602-2-22-2-222-2220000-22-2-222-200002-200-2-22200000022-2-200000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ6144-4-44i−4i4i−4i000004-40000000004i−4i00002-22-22-22-2002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6244-4-44i−4i4i−4i000004-40000000004i−4i0000-22-22-22-2200−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6344-4-44i−4i4i−4i00000-44000000000−4i4i00002-22-2-22-22002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6444-4-44i−4i4i−4i00000-44000000000−4i4i0000-22-222-22-200−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6544-4-4−4i4i−4i4i000004-4000000000−4i4i00002-22-22-22-200−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6644-4-4−4i4i−4i4i000004-4000000000−4i4i0000-22-22-22-22002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6744-4-4−4i4i−4i4i00000-440000000004i−4i00002-22-2-22-2200−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6844-4-4−4i4i−4i4i00000-440000000004i−4i0000-22-222-22-2002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ694-44-44i−4i−4i4i0004-40000000004i−4i0000002-2-222-2-22002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ704-44-44i−4i−4i4i0004-40000000004i−4i000000-222-2-222-200−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ714-44-44i−4i−4i4i000-44000000000−4i4i0000002-2-22-222-2002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ724-44-44i−4i−4i4i000-44000000000−4i4i000000-222-22-2-2200−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ734-44-4−4i4i4i−4i0004-4000000000−4i4i0000002-2-222-2-2200−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ744-44-4−4i4i4i−4i0004-4000000000−4i4i000000-222-2-222-2002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ754-44-4−4i4i4i−4i000-440000000004i−4i0000002-2-22-222-200−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ764-44-4−4i4i4i−4i000-440000000004i−4i000000-222-22-2-22002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ774-4-4444-4-44-4-40000-444-44-4400004-40000000000000000000000000000000000000000000000000000
χ784-4-4444-4-4-44-400004-44-444-40000-440000000000000000000000000000000000000000000000000000
χ794-4-44-4-4444-4-40000-4444-44-40000-440000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-44-400004-444-4-4400004-40000000000000000000000000000000000000000000000000000

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