Finite Group Databasebeta

← Group #321392

Character table — Group #321392

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888444444442244
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ121111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222-2-2-2-2-2-222-2-222-2-2-2-200000000000000000000000022-2-222-2-2000000000000
χ1822222222222222-2-2-2-2-2-222-2-222-2-2-2-2000000000000000000000000-2-222-2-222000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000022-2-2-2-222000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000-2-22222-2-2000000000000
χ2122222222-2-2222222-2-2-2-2-2-222-2-2-2-222000000000000000022-2-222-2-200000000000000000000
χ2222222222-2-2222222-2-2-2-2-2-222-2-2-2-2220000000000000000-2-222-2-22200000000000000000000
χ2322222222-2-22222-2-22222-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2422222222-2-22222-2-22222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-20000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ29222-2-22-2-20022-2-20022-2-20000002-200000022-2-2000022-2-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ30222-2-22-2-20022-2-20022-2-20000002-200000022-2-2000022-2-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ31222-2-22-2-20022-2-20022-2-20000002-2000000-2-2220000-2-222i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ32222-2-22-2-20022-2-20022-2-20000002-2000000-2-2220000-2-222−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ33222-2-22-2-20022-2-200-2-222000000-220022-2-2000022-2-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ34222-2-22-2-20022-2-200-2-222000000-220022-2-2000022-2-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ35222-2-22-2-20022-2-200-2-222000000-2200-2-2220000-2-2220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ36222-2-22-2-20022-2-200-2-222000000-2200-2-2220000-2-2220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ37222-2-22-2-200-2-2220022-2-2000000-2200000022-2-20000-2-222i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ38222-2-22-2-200-2-2220022-2-2000000-2200000022-2-20000-2-222−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ39222-2-22-2-200-2-2220022-2-2000000-22000000-2-222000022-2-2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ40222-2-22-2-200-2-2220022-2-2000000-22000000-2-222000022-2-2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ41222-2-22-2-200-2-22200-2-2220000002-20022-2-20000-2-2220000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ42222-2-22-2-200-2-22200-2-2220000002-20022-2-20000-2-2220000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ43222-2-22-2-200-2-22200-2-2220000002-200-2-222000022-2-20000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ44222-2-22-2-200-2-22200-2-2220000002-200-2-222000022-2-20000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ452-2-22-222-2220000222-22-2-2-2-2-2000000000000002-22-22-22-20000000000000000002i−2i2i−2i000000
χ462-2-22-222-2220000222-22-2-2-2-2-2000000000000002-22-22-22-2000000000000000000−2i2i−2i2i000000
χ472-2-22-222-2220000222-22-2-2-2-2-200000000000000-22-22-22-220000000000000000002i−2i−2i2i000000
χ482-2-22-222-2220000222-22-2-2-2-2-200000000000000-22-22-22-22000000000000000000−2i2i2i−2i000000
χ492-2-22-222-2-2-20000-2-22-22-22222000000000000002-22-2-22-2200000000000000002-200002-20000
χ502-2-22-222-2-2-20000-2-22-22-22222000000000000002-22-2-22-220000000000000000-220000-220000
χ512-2-22-222-2-2-20000-2-22-22-2222200000000000000-22-222-22-200000000000000002-20000-220000
χ522-2-22-222-2-2-20000-2-22-22-2222200000000000000-22-222-22-20000000000000000-2200002-20000
χ5344-444-4-4-44-400000000004-40000000022−2222−2222−2222−22000000000000000000000000000000000000
χ5444-444-4-4-44-400000000004-400000000−2222−2222−2222−2222000000000000000000000000000000000000
χ5544-444-4-4-4-440000000000-440000000022−2222−22−2222−2222000000000000000000000000000000000000
χ5644-444-4-4-4-440000000000-4400000000−2222−222222−2222−22000000000000000000000000000000000000
χ5744-4-4-4-4440000004-40000004-400000022−22−222222−22−2222000000000000000000000000000000000000
χ5844-4-4-4-4440000004-40000004-4000000−222222−22−222222−22000000000000000000000000000000000000
χ5944-4-4-4-444000000-44000000-4400000022−22−2222−222222−22000000000000000000000000000000000000
χ6044-4-4-4-444000000-44000000-44000000−222222−2222−22−2222000000000000000000000000000000000000
χ614-444-4-4-444-44i−4i4i−4i000000-44004i−4i000000000000000000000000000000000000000000000000
χ624-444-4-4-444-4−4i4i−4i4i000000-4400−4i4i000000000000000000000000000000000000000000000000
χ634-444-4-4-44-444i−4i4i−4i0000004-400−4i4i000000000000000000000000000000000000000000000000
χ644-444-4-4-44-44−4i4i−4i4i0000004-4004i−4i000000000000000000000000000000000000000000000000
χ654-44-44-44-4004i−4i−4i4i4-4000000-4400004i−4i00000000000000000000000000000000000000000000
χ664-44-44-44-4004i−4i−4i4i-440000004-40000−4i4i00000000000000000000000000000000000000000000
χ674-44-44-44-400−4i4i4i−4i4-4000000-440000−4i4i00000000000000000000000000000000000000000000
χ684-44-44-44-400−4i4i4i−4i-440000004-400004i−4i00000000000000000000000000000000000000000000
χ694-4-44-444-4440000-4-4-44-44-4-44400000000000000000000000000000000000000000000000000
χ704-4-44-444-4-4-4000044-44-4444-4-400000000000000000000000000000000000000000000000000
χ714-4-4-444-44000000004-4-4400000000000000000000004-4-440000000000000000000000000000
χ724-4-4-444-44000000004-4-440000000000000000000000-444-40000000000000000000000000000
χ734-4-4-444-4400000000-444-40000000000000000004-4-4400000000000000000000000000000000
χ744-4-4-444-4400000000-444-4000000000000000000-444-400000000000000000000000000000000

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