Finite Group Databasebeta

← Group #321309

Character table — Group #321309

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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ91111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11
χ111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11
χ121111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1
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
χ29222-2-2-2-222200002222-2-2-2-2-2-200000022-2-222-2-20000000000000000000000002i−2i2i−2i00000000
χ30222-2-2-2-222200002222-2-2-2-2-2-200000022-2-222-2-2000000000000000000000000−2i2i−2i2i00000000
χ31222-2-2-2-222200002222-2-2-2-2-2-2000000-2-222-2-2220000000000000000000000002i−2i−2i2i00000000
χ32222-2-2-2-222200002222-2-2-2-2-2-2000000-2-222-2-222000000000000000000000000−2i2i2i−2i00000000
χ33222-2-2-2-22-2-20000-2-222-2-2222200000022-2-2-2-22200000000000000000000000000002-22-20000
χ34222-2-2-2-22-2-20000-2-222-2-2222200000022-2-2-2-2220000000000000000000000000000-22-220000
χ35222-2-2-2-22-2-20000-2-222-2-22222000000-2-22222-2-200000000000000000000000000002-2-220000
χ36222-2-2-2-22-2-20000-2-222-2-22222000000-2-22222-2-20000000000000000000000000000-222-20000
χ372-2-22-2-2220022-2-22-20000002-200002-22−22−22−22−222−2−222−2−2002-2002-22−22−22−22−2000000000000
χ382-2-22-2-2220022-2-22-20000002-200002-22−22−22−22−222−2−222−2−200-2200-22−22−22−22−22000000000000
χ392-2-22-2-2220022-2-22-20000002-200002-2−22−22−22−22−2−222−2−222002-2002-2−22−22−22−22000000000000
χ402-2-22-2-2220022-2-22-20000002-200002-2−22−22−22−22−2−222−2−22200-2200-222−22−22−22−2000000000000
χ412-2-22-2-2220022-2-2-22000000-220000-222−22−2−22−2222−2−2−2−2222-2002-2002−2−222−2−22000000000000
χ422-2-22-2-2220022-2-2-22000000-220000-222−22−2−22−2222−2−2−2−222-2200-2200−222−2−222−2000000000000
χ432-2-22-2-2220022-2-2-22000000-220000-22−22−222−22−2−2−22222−2−22-2002-200−222−2−222−2000000000000
χ442-2-22-2-2220022-2-2-22000000-220000-22−22−222−22−2−2−22222−2−2-2200-22002−2−222−2−22000000000000
χ452-2-22-2-22200-2-2222-20000002-20000-222−22−22−22−2−2−222−2−222002-200-222−22−2−22−22000000000000
χ462-2-22-2-22200-2-2222-20000002-20000-222−22−22−22−2−2−222−2−22200-22002-2−22−222−22−2000000000000
χ472-2-22-2-22200-2-2222-20000002-20000-22−22−22−22−2222−2−222−2−2002-200-22−22−222−22−2000000000000
χ482-2-22-2-22200-2-2222-20000002-20000-22−22−22−22−2222−2−222−2−200-22002-22−22−2−22−22000000000000
χ492-2-22-2-22200-2-222-22000000-2200002-22−22−2−22−22−2−22222−2−22-200-22002−2−22−222−2000000000000
χ502-2-22-2-22200-2-222-22000000-2200002-22−22−2−22−22−2−22222−2−2-22002-200−222−22−2−22000000000000
χ512-2-22-2-22200-2-222-22000000-2200002-2−22−222−22−222−2−2−2−2222-200-2200−222−22−2−22000000000000
χ522-2-22-2-22200-2-222-22000000-2200002-2−22−222−22−222−2−2−2−222-22002-2002−2−22−222−2000000000000
χ53444-4-4-4-44440000-4-4-4-444-4-44400000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-4000044-4-44444-4-400000000000000000000000000000000000000000000000000
χ5544-444-4-4-4004-44-4004-44-40000004-40000000000000000000000000000000000000000000000
χ5644-444-4-4-4004-44-400-44-44000000-440000000000000000000000000000000000000000000000
χ5744-444-4-4-400-44-44004-44-4000000-440000000000000000000000000000000000000000000000
χ5844-444-4-4-400-44-4400-44-440000004-40000000000000000000000000000000000000000000000
χ5944-4-4-444-4000000004-4-440000000000000000004i−4i4i−4i00000000000000000000000000000000
χ6044-4-4-444-4000000004-4-44000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ6144-4-4-444-400000000-444-400000000000000000000004i−4i4i−4i0000000000000000000000000000
χ6244-4-4-444-400000000-444-40000000000000000000000−4i4i−4i4i0000000000000000000000000000
χ634-444-44-4-44-44-4-440000004-4004-4000000000000000000000000000000000000000000000000
χ644-444-44-4-44-4-444-40000004-400-44000000000000000000000000000000000000000000000000
χ654-444-44-4-4-444-4-44000000-4400-44000000000000000000000000000000000000000000000000
χ664-444-44-4-4-44-444-4000000-44004-4000000000000000000000000000000000000000000000000
χ674-44-44-44-44-40000000000-4400000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ684-44-44-44-44-40000000000-440000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ694-44-44-44-4-4400000000004-400000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ704-44-44-44-4-4400000000004-40000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ714-4-4-444-440000004-4000000-4400000022−22−222222−22−2222000000000000000000000000000000000000
χ724-4-4-444-440000004-4000000-44000000−222222−22−222222−22000000000000000000000000000000000000
χ734-4-4-444-44000000-440000004-400000022−22−2222−222222−22000000000000000000000000000000000000
χ744-4-4-444-44000000-440000004-4000000−222222−2222−22−2222000000000000000000000000000000000000

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