Finite Group Databasebeta

← Group #413894

Character table — Group #413894

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222222222444444444422222222444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-11111-1-111-1-111-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111111111-1-111-1-1-1-111
χ172222222222-2-2-2-222-2-2-2-2222222-2-2-2-2000000002222-2-2000000000000-2-20000000000000000
χ182222222222-2-2-2-222-2-2-2-2222222-2-2-2-200000000-2-2-2-222000000000000220000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222220000000022-2-222000000000000-2-20000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2222200000000-2-222-2-2000000000000220000000000000000
χ2122222222-2-222-2-2-2-222-2-22222-2-222-2-2000000220000000000-2-2-2-20000000022000000000000
χ2222222222-2-222-2-2-2-222-2-22222-2-222-2-2000000-2-20000000000222200000000-2-2000000000000
χ2322222222-2-222-2-2-2-222-2-2-2-2-2-222-2-222000000220000000000-2-22200000000-2-2000000000000
χ2422222222-2-222-2-2-2-222-2-2-2-2-2-222-2-222000000-2-2000000000022-2-20000000022000000000000
χ2522222222-2-2-2-222-2-2-2-2222222-2-2-2-22200002200000000-2-2-2-200000000002200000000000000
χ2622222222-2-2-2-222-2-2-2-2222222-2-2-2-2220000-2-20000000022220000000000-2-200000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-22222-2-200002200000000-2-2220000000000-2-200000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-22222-2-20000-2-20000000022-2-200000000002200000000000000
χ29222-22-2-2-22-22-22-22-22-22-22i2i−2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000002i−2i2-2
χ30222-22-2-2-22-22-22-22-22-22-22i2i−2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000−2i2i-22
χ31222-22-2-2-22-22-22-22-22-22-2−2i−2i2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000002i−2i-22
χ32222-22-2-2-22-22-22-22-22-22-2−2i−2i2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000−2i2i2-2
χ33222-22-2-2-22-2-22-222-2-22-222i2i−2i−2i2i−2i−2i2i−2i2i22-2-20000000000000000002i2i−2i−2i000000000000000000
χ34222-22-2-2-22-2-22-222-2-22-222i2i−2i−2i2i−2i−2i2i−2i2i-2-222000000000000000000−2i−2i2i2i000000000000000000
χ35222-22-2-2-22-2-22-222-2-22-22−2i−2i2i2i−2i2i2i−2i2i−2i22-2-2000000000000000000−2i−2i2i2i000000000000000000
χ36222-22-2-2-22-2-22-222-2-22-22−2i−2i2i2i−2i2i2i−2i2i−2i-2-2220000000000000000002i2i−2i−2i000000000000000000
χ37222-22-2-2-2-222-2-22-222-2-222i2i−2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002-22i−2i00000000
χ38222-22-2-2-2-222-2-22-222-2-222i2i−2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000-22−2i2i00000000
χ39222-22-2-2-2-222-2-22-222-2-22−2i−2i2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002-2−2i2i00000000
χ40222-22-2-2-2-222-2-22-222-2-22−2i−2i2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000-222i−2i00000000
χ41222-22-2-2-2-22-222-2-22-222-22i2i−2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000002-22i−2i0000
χ42222-22-2-2-2-22-222-2-22-222-22i2i−2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000-22−2i2i0000
χ43222-22-2-2-2-22-222-2-22-222-2−2i−2i2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000002-2−2i2i0000
χ44222-22-2-2-2-22-222-2-22-222-2−2i−2i2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000-222i−2i0000
χ452-2-222-22-22222-2-2-2-2-2-222000000000000002-200002i−2i2i−2i2-200002i−2i000000002i−2i000000000000
χ462-2-222-22-22222-2-2-2-2-2-222000000000000002-20000−2i2i−2i2i2-20000−2i2i00000000−2i2i000000000000
χ472-2-222-22-22222-2-2-2-2-2-22200000000000000-2200002i−2i2i−2i-220000−2i2i00000000−2i2i000000000000
χ482-2-222-22-22222-2-2-2-2-2-22200000000000000-220000−2i2i−2i2i-2200002i−2i000000002i−2i000000000000
χ492-2-222-22-222-2-222-2-222-2-200000000000000002-2002i−2i−2i2i002i−2i2-2000000002i−2i00000000000000
χ502-2-222-22-222-2-222-2-222-2-200000000000000002-200−2i2i2i−2i00−2i2i2-200000000−2i2i00000000000000
χ512-2-222-22-222-2-222-2-222-2-20000000000000000-22002i−2i−2i2i00−2i2i-2200000000−2i2i00000000000000
χ522-2-222-22-222-2-222-2-222-2-20000000000000000-2200−2i2i2i−2i002i−2i-22000000002i−2i00000000000000
χ532-2-222-22-2-2-2222222-2-2-2-20000000000000000002-20000002i−2i002i−2i00002-2−2i2i−2i2i000000000000
χ542-2-222-22-2-2-2222222-2-2-2-20000000000000000002-2000000−2i2i00−2i2i00002-22i−2i2i−2i000000000000
χ552-2-222-22-2-2-2222222-2-2-2-2000000000000000000-220000002i−2i00−2i2i0000-22−2i2i2i−2i000000000000
χ562-2-222-22-2-2-2222222-2-2-2-2000000000000000000-22000000−2i2i002i−2i0000-222i−2i−2i2i000000000000
χ572-2-222-22-2-2-2-2-2-2-2222222000000000000002-22-22-20000-2200-22000000-220000000000000000
χ582-2-222-22-2-2-2-2-2-2-2222222000000000000002-2-22-220000-22002-20000002-20000000000000000
χ592-2-222-22-2-2-2-2-2-2-222222200000000000000-222-2-2200002-200-220000002-20000000000000000
χ602-2-222-22-2-2-2-2-2-2-222222200000000000000-22-222-200002-2002-2000000-220000000000000000
χ6144-44-44-4-40000000000004i−4i4i−4i0000002-22-20000000000000000002i−2i2i−2i000000000000000000
χ6244-44-44-4-40000000000004i−4i4i−4i000000-22-22000000000000000000−2i2i−2i2i000000000000000000
χ6344-44-44-4-4000000000000−4i4i−4i4i0000002-22-2000000000000000000−2i2i−2i2i000000000000000000
χ6444-44-44-4-4000000000000−4i4i−4i4i000000-22-220000000000000000002i−2i2i−2i000000000000000000
χ6544-4-4-4-4440000000000004-4-440000002-2-220000000000000000002-2-22000000000000000000
χ6644-4-4-4-4440000000000004-4-44000000-222-2000000000000000000-222-2000000000000000000
χ6744-4-4-4-444000000000000-444-40000002-2-22000000000000000000-222-2000000000000000000
χ6844-4-4-4-444000000000000-444-4000000-222-20000000000000000002-2-22000000000000000000
χ694-4-4-444-444-44-4-44-44-444-4000000000000000000000000000000000000000000000000000000
χ704-4-4-444-444-4-444-4-444-4-44000000000000000000000000000000000000000000000000000000
χ714-4-4-444-44-444-44-44-4-44-44000000000000000000000000000000000000000000000000000000
χ724-4-4-444-44-44-44-444-44-44-4000000000000000000000000000000000000000000000000000000
χ738-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000

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