Finite Group Databasebeta

← Group #396296

Character table — Group #396296

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422444444444444448888888888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ9111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ10111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ11111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000000000002i−2i2i−2i00
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000000000−2i2i−2i2i00
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000002i−2i−2i2i00
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000−2i2i2i−2i00
χ2122222222-2-2-2-2222222-2-2-222-2-2-222-2-200000000000000000000000022-2-222-2-2000000000000
χ2222222222-2-2-2-2222222-2-2-222-2-2-222-2-2000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-2-2-22222-2-2222-2-22-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2222-2-22-2-2-2-222-2-2-2-22222000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-222-222-2-22200000000000000000000000022-2-2-2-222000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-222-222-2-222000000000000000000000000-2-22222-2-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222-2-222222-2-222-2-2-2-222000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222-2-222222-2-2-2-22222-2-2000000000000000000000000000000000000
χ29222-2-2-22-222-2-22i2i−2i−2i2-22-2-22-222i−2i2i−2i2i−2i00000000000000002i2i−2i−2i22-2-200000000000000000000
χ30222-2-2-22-222-2-22i2i−2i−2i2-22-2-22-222i−2i2i−2i2i−2i0000000000000000−2i−2i2i2i-2-22200000000000000000000
χ31222-2-2-22-222-2-22i2i−2i−2i-22-222-22-22i−2i−2i2i−2i2i000000000000000000000000000000002-22i−2i00000000
χ32222-2-2-22-222-2-22i2i−2i−2i-22-222-22-22i−2i−2i2i−2i2i00000000000000000000000000000000-22−2i2i00000000
χ33222-2-2-22-222-2-2−2i−2i2i2i2-22-2-22-22−2i2i−2i2i−2i2i00000000000000002i2i−2i−2i-2-22200000000000000000000
χ34222-2-2-22-222-2-2−2i−2i2i2i2-22-2-22-22−2i2i−2i2i−2i2i0000000000000000−2i−2i2i2i22-2-200000000000000000000
χ35222-2-2-22-222-2-2−2i−2i2i2i-22-222-22-2−2i2i2i−2i2i−2i000000000000000000000000000000002-2−2i2i00000000
χ36222-2-2-22-222-2-2−2i−2i2i2i-22-222-22-2−2i2i2i−2i2i−2i00000000000000000000000000000000-222i−2i00000000
χ37222-2-2-22-2-2-2222i2i−2i−2i2-2-2222-2-2−2i2i2i−2i−2i2i0000000000000000000000000000000000002-200002i−2i
χ38222-2-2-22-2-2-2222i2i−2i−2i2-2-2222-2-2−2i2i2i−2i−2i2i000000000000000000000000000000000000-220000−2i2i
χ39222-2-2-22-2-2-2222i2i−2i−2i-222-2-2-222−2i2i−2i2i2i−2i000000002i2i−2i−2i22-2-20000000000000000000000000000
χ40222-2-2-22-2-2-2222i2i−2i−2i-222-2-2-222−2i2i−2i2i2i−2i00000000−2i−2i2i2i-2-2220000000000000000000000000000
χ41222-2-2-22-2-2-222−2i−2i2i2i2-2-2222-2-22i−2i−2i2i2i−2i0000000000000000000000000000000000002-20000−2i2i
χ42222-2-2-22-2-2-222−2i−2i2i2i2-2-2222-2-22i−2i−2i2i2i−2i000000000000000000000000000000000000-2200002i−2i
χ43222-2-2-22-2-2-222−2i−2i2i2i-222-2-2-2222i−2i2i−2i−2i2i000000002i2i−2i−2i-2-2220000000000000000000000000000
χ44222-2-2-22-2-2-222−2i−2i2i2i-222-2-2-2222i−2i2i−2i−2i2i00000000−2i−2i2i2i22-2-20000000000000000000000000000
χ452-2-222-22-22-22-2000022-22-2-2-220000002-2002-2002i−2i2i−2i00002i−2i2i−2i000000000000000000000000
χ462-2-222-22-22-22-2000022-22-2-2-220000002-2002-200−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000
χ472-2-222-22-22-22-2000022-22-2-2-22000000-2200-22002i−2i2i−2i0000−2i2i−2i2i000000000000000000000000
χ482-2-222-22-22-22-2000022-22-2-2-22000000-2200-2200−2i2i−2i2i00002i−2i2i−2i000000000000000000000000
χ492-2-222-22-2-22-220000-2-2-22-22220000002-200-220000002-22-200002-22-200000000000000000000
χ502-2-222-22-2-22-220000-2-2-22-22220000002-200-22000000-22-220000-22-2200000000000000000000
χ512-2-222-22-2-22-220000-2-2-22-2222000000-22002-20000002-22-20000-22-2200000000000000000000
χ522-2-222-22-2-22-220000-2-2-22-2222000000-22002-2000000-22-2200002-22-200000000000000000000
χ532-2-2-2-22222-2-2200002-2-2-22-222000000002-2002-200002-2-222-2-22000000000000000000000000
χ542-2-2-2-22222-2-2200002-2-2-22-222000000002-2002-20000-222-2-222-2000000000000000000000000
χ552-2-2-2-22222-2-2200002-2-2-22-22200000000-2200-2200002-2-22-222-2000000000000000000000000
χ562-2-2-2-22222-2-2200002-2-2-22-22200000000-2200-220000-222-22-2-22000000000000000000000000
χ572-2-2-2-2222-222-20000-22-2-222-22000000002-200-222-2-22000000002-2-2200000000000000000000
χ582-2-2-2-2222-222-20000-22-2-222-22000000002-200-22-222-200000000-222-200000000000000000000
χ592-2-2-2-2222-222-20000-22-2-222-2200000000-22002-22-2-2200000000-222-200000000000000000000
χ602-2-2-2-2222-222-20000-22-2-222-2200000000-22002-2-222-2000000002-2-2200000000000000000000
χ6144-44-4-4-4400004i−4i4i−4i000000000000000000000000000000000000000022−22002i2−2i2000000000000
χ6244-44-4-4-4400004i−4i4i−4i0000000000000000000000000000000000000000−222200−2i22i2000000000000
χ6344-44-4-4-440000−4i4i−4i4i000000000000000000000000000000000000000022−2200−2i22i2000000000000
χ6444-44-4-4-440000−4i4i−4i4i0000000000000000000000000000000000000000−2222002i2−2i2000000000000
χ6544-4-444-4-400004-4-44000000000000000000000000000000000000002i2−2i2002i2−2i200000000000000
χ6644-4-444-4-400004-4-4400000000000000000000000000000000000000−2i22i200−2i22i200000000000000
χ6744-4-444-4-40000-444-4000000000000000000000000000000000000002i2−2i200−2i22i200000000000000
χ6844-4-444-4-40000-444-400000000000000000000000000000000000000−2i22i2002i2−2i200000000000000
χ694-4-444-44-44-44-40000-4-44-4444-400000000000000000000000000000000000000000000000000
χ704-4-444-44-4-44-440000444-44-4-4-400000000000000000000000000000000000000000000000000
χ714-4-4-4-44444-4-440000-4444-44-4-400000000000000000000000000000000000000000000000000
χ724-4-4-4-4444-444-400004-444-4-44-400000000000000000000000000000000000000000000000000
χ738-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000

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