Finite Group Databasebeta

← Group #321449

Character table — Group #321449

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444444444444444488888888888888888888888844888888888888444444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1111-11-1
χ911111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ1011111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-111-1-1-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ172222222222-2-2-2-2-2-222-2-222-2-2000000002222-2-2-2-200000000-22000022-2-20000000000000000
χ182222222222-2-2-2-2-2-222-2-222-2-200000000-2-2-2-2222200000000-220000-2-2220000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-222000000002222-2-2-2-2000000002-20000-2-2220000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-22200000000-2-2-2-22222000000002-2000022-2-20000000000000000
χ2122222222-2-222-2-2-2-2-2-22222-2-200000000000000002222-2-2-2-22-20000000022-2-2000000000000
χ2222222222-2-222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-222222-200000000-2-222000000000000
χ2322222222-2-222-2-2-2-2-2-222-2-22200000000000000002222-2-2-2-2-2200000000-2-222000000000000
χ2422222222-2-222-2-2-2-2-2-222-2-2220000000000000000-2-2-2-22222-220000000022-2-2000000000000
χ2522222222-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000-2-222-2-200000000000000000000
χ2622222222-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000-2-2-2-22200000000000000000000
χ2722222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022-2-22200000000000000000000
χ2822222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-200000000000000000000
χ2922-2-22-22-2000022-2-200002i−2i2i−2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200002-22−22−2i2−i2i2−i2000000000000
χ3022-2-22-22-2000022-2-200002i−2i2i−2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200002-2−22−22−i2i2−i2i2000000000000
χ3122-2-22-22-2000022-2-200002i−2i2i−2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000-222−22−2−i2i2−i2i2000000000000
χ3222-2-22-22-2000022-2-200002i−2i2i−2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000-22−22−22i2−i2i2−i2000000000000
χ3322-2-22-22-2000022-2-20000−2i2i−2i2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000-22−22−22−i2i2−i2i2000000000000
χ3422-2-22-22-2000022-2-20000−2i2i−2i2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000-222−22−2i2−i2i2−i2000000000000
χ3522-2-22-22-2000022-2-20000−2i2i−2i2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200002-2−22−22i2−i2i2−i2000000000000
χ3622-2-22-22-2000022-2-20000−2i2i−2i2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200002-22−22−2−i2i2−i2i2000000000000
χ3722-2-22-22-20000-2-22200002i−2i−2i2i2i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−222002-2002−2−22i2−i2−i2i2000000000000
χ3822-2-22-22-20000-2-22200002i−2i−2i2i2i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2002-200−222−2−i2i2i2−i2000000000000
χ3922-2-22-22-20000-2-22200002i−2i−2i2i−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200-22002−2−22−i2i2i2−i2000000000000
χ4022-2-22-22-20000-2-22200002i−2i−2i2i−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200-2200−222−2i2−i2−i2i2000000000000
χ4122-2-22-22-20000-2-2220000−2i2i2i−2i2i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200-2200−222−2−i2i2i2−i2000000000000
χ4222-2-22-22-20000-2-2220000−2i2i2i−2i2i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200-22002−2−22i2−i2−i2i2000000000000
χ4322-2-22-22-20000-2-2220000−2i2i2i−2i−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2002-200−222−2i2−i2−i2i2000000000000
χ4422-2-22-22-20000-2-2220000−2i2i2i−2i−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−222002-2002−2−22−i2i2i2−i2000000000000
χ452-22-2-2-22222222-22-2-2-2-2-200002-22-22-22-20000000000000000000000000000002i−2i2i−2i00000000
χ462-22-2-2-22222222-22-2-2-2-2-200002-22-22-22-2000000000000000000000000000000−2i2i−2i2i00000000
χ472-22-2-2-22222222-22-2-2-2-2-20000-22-22-22-220000000000000000000000000000002i−2i−2i2i00000000
χ482-22-2-2-22222222-22-2-2-2-2-20000-22-22-22-22000000000000000000000000000000−2i2i2i−2i00000000
χ492-22-2-2-222-2-2-2-22-22-2222200002-22-2-22-2200000000000000000000000000000000002-22-20000
χ502-22-2-2-222-2-2-2-22-22-2222200002-22-2-22-220000000000000000000000000000000000-22-220000
χ512-22-2-2-222-2-2-2-22-22-222220000-22-222-22-200000000000000000000000000000000002-2-220000
χ522-22-2-2-222-2-2-2-22-22-222220000-22-222-22-20000000000000000000000000000000000-222-20000
χ53444-4-44-4-44-40000004-40000000000000000004-44-40000000000000000000000000000000000
χ54444-4-44-4-44-40000004-4000000000000000000-44-440000000000000000000000000000000000
χ55444-4-44-4-4-44000000-44000000000000004-44-400000000000000000000000000000000000000
χ56444-4-44-4-4-44000000-4400000000000000-44-4400000000000000000000000000000000000000
χ5744-44-4-4-44004-40000004-40000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ5844-44-4-4-44004-40000004-4000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ5944-44-4-4-4400-44000000-440000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ6044-44-4-4-4400-44000000-44000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ614-4444-4-4-44-4000000-44000000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ624-4444-4-4-44-4000000-440000000000000000000000−2222−2222−2222−222200000000000000000000000000
χ634-4444-4-4-4-440000004-4000000000000000000000022−2222−22−2222−222200000000000000000000000000
χ644-4444-4-4-4-440000004-40000000000000000000000−2222−222222−2222−2200000000000000000000000000
χ654-44-4-4-44444-4-4-44-44-4-444000000000000000000000000000000000000000000000000000000
χ664-44-4-4-444-4-444-44-4444-4-4000000000000000000000000000000000000000000000000000000
χ674-4-44-444-400004-4-440000000000004i−4i−4i4i000000000000000000000000000000000000000000
χ684-4-44-444-400004-4-44000000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ694-4-44-444-40000-444-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ704-4-44-444-40000-444-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ714-4-4-444-44004-4000000-440000000000000000000000004-4-4400000000000000000000000000
χ724-4-4-444-44004-4000000-44000000000000000000000000-444-400000000000000000000000000
χ734-4-4-444-4400-440000004-4000000000000000000004-4-44000000000000000000000000000000
χ744-4-4-444-4400-440000004-400000000000000000000-444-4000000000000000000000000000000

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