Finite Group Databasebeta

← Group #323321

Character table — Group #323321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888444444444444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ9111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ10111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ11111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ12111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ172222222222-2-22222-2-2-2-222-2-222-2-2-2-200000000000000000000000022-2-222-2-2000000000000
χ182222222222-2-22222-2-2-2-222-2-222-2-2-2-2000000000000000000000000-2-222-2-222000000000000
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
χ2322222222-2-222-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000022-2-2-2-22200000000000000000000
χ2422222222-2-222-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000-2-22222-2-200000000000000000000
χ2522222222-2-2-2-222222222-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2622222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
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
χ29222-2-22-2-22222000022-2-2-2-2-2-200000022-2-222-2-20000000000000000000000002-22-200000000
χ30222-2-22-2-22222000022-2-2-2-2-2-200000022-2-222-2-2000000000000000000000000-22-2200000000
χ31222-2-22-2-22222000022-2-2-2-2-2-2000000-2-222-2-2220000000000000000000000002-2-2200000000
χ32222-2-22-2-22222000022-2-2-2-2-2-2000000-2-222-2-222000000000000000000000000-222-200000000
χ33222-2-22-2-2-2-2-2-2000022-2-2222200000022-2-2-2-22200000000000000000000000000002i−2i2i−2i0000
χ34222-2-22-2-2-2-2-2-2000022-2-2222200000022-2-2-2-2220000000000000000000000000000−2i2i−2i2i0000
χ35222-2-22-2-2-2-2-2-2000022-2-22222000000-2-22222-2-200000000000000000000000000002i−2i−2i2i0000
χ36222-2-22-2-2-2-2-2-2000022-2-22222000000-2-22222-2-20000000000000000000000000000−2i2i2i−2i0000
χ372-2-2-2-2222002-222-2-20000002-200002-22−22−22−22−222−2−222−2−2002-2002-22−22−22−22−2000000000000
χ382-2-2-2-2222002-222-2-20000002-200002-22−22−22−22−222−2−222−2−200-2200-22−22−22−22−22000000000000
χ392-2-2-2-2222002-222-2-20000002-200002-2−22−22−22−22−2−222−2−222002-2002-2−22−22−22−22000000000000
χ402-2-2-2-2222002-222-2-20000002-200002-2−22−22−22−22−2−222−2−22200-2200-222−22−22−22−2000000000000
χ412-2-2-2-2222002-2-2-2220000002-20000-222−22−22−22−2−2−222−2−222002-200-222−22−2−22−22000000000000
χ422-2-2-2-2222002-2-2-2220000002-20000-222−22−22−22−2−2−222−2−22200-22002-2−22−222−22−2000000000000
χ432-2-2-2-2222002-2-2-2220000002-20000-22−22−22−22−2222−2−222−2−2002-200-22−22−222−22−2000000000000
χ442-2-2-2-2222002-2-2-2220000002-20000-22−22−22−22−2222−2−222−2−200-22002-22−22−2−22−22000000000000
χ452-2-2-2-222200-2222-2-2000000-220000-222−22−2−22−2222−2−2−2−2222-2002-2002−2−222−2−22000000000000
χ462-2-2-2-222200-2222-2-2000000-220000-222−22−2−22−2222−2−2−2−222-2200-2200−222−2−222−2000000000000
χ472-2-2-2-222200-2222-2-2000000-220000-22−22−222−22−2−2−22222−2−22-2002-200−222−2−222−2000000000000
χ482-2-2-2-222200-2222-2-2000000-220000-22−22−222−22−2−2−22222−2−2-2200-22002−2−222−2−22000000000000
χ492-2-2-2-222200-22-2-222000000-2200002-22−22−2−22−22−2−22222−2−22-200-22002−2−22−222−2000000000000
χ502-2-2-2-222200-22-2-222000000-2200002-22−22−2−22−22−2−22222−2−2-22002-200−222−22−2−22000000000000
χ512-2-2-2-222200-22-2-222000000-2200002-2−22−222−22−222−2−2−2−2222-200-2200−222−22−2−22000000000000
χ522-2-2-2-222200-22-2-222000000-2200002-2−22−222−22−222−2−2−2−222-22002-2002−2−22−222−2000000000000
χ53444-4-44-4-444-4-40000-4-444-4-44400000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-4-4440000-4-44444-4-400000000000000000000000000000000000000000000000000
χ5544-44-4-44-4000000004-44-40000000000000000004-44-400000000000000000000000000000000
χ5644-44-4-44-4000000004-44-4000000000000000000-44-4400000000000000000000000000000000
χ5744-44-4-44-400000000-44-4400000000000000000000004-44-40000000000000000000000000000
χ5844-44-4-44-400000000-44-440000000000000000000000-44-440000000000000000000000000000
χ5944-4-44-4-4400004i−4i4i−4i4-4-440000004i−4i0000000000000000000000000000000000000000000000
χ6044-4-44-4-4400004i−4i4i−4i-444-4000000−4i4i0000000000000000000000000000000000000000000000
χ6144-4-44-4-440000−4i4i−4i4i4-4-44000000−4i4i0000000000000000000000000000000000000000000000
χ6244-4-44-4-440000−4i4i−4i4i-444-40000004i−4i0000000000000000000000000000000000000000000000
χ634-444-4-4-444-4004i−4i−4i4i00004-4004i−4i000000000000000000000000000000000000000000000000
χ644-444-4-4-444-400−4i4i4i−4i00004-400−4i4i000000000000000000000000000000000000000000000000
χ654-444-4-4-44-44004i−4i−4i4i0000-4400−4i4i000000000000000000000000000000000000000000000000
χ664-444-4-4-44-4400−4i4i4i−4i0000-44004i−4i000000000000000000000000000000000000000000000000
χ674-44-44-44-44-40000000000-44000000000000000022−22−222222−22−22220000000000000000000000000000
χ684-44-44-44-44-40000000000-440000000000000000−222222−22−222222−220000000000000000000000000000
χ694-44-44-44-4-4400000000004-4000000000000000022−22−2222−222222−220000000000000000000000000000
χ704-44-44-44-4-4400000000004-40000000000000000−222222−2222−22−22220000000000000000000000000000
χ714-4-4444-4-4004-40000000000-4400000022−22−222222−22−2222000000000000000000000000000000000000
χ724-4-4444-4-4004-40000000000-44000000−222222−22−222222−22000000000000000000000000000000000000
χ734-4-4444-4-400-4400000000004-400000022−22−2222−222222−22000000000000000000000000000000000000
χ744-4-4444-4-400-4400000000004-4000000−222222−2222−22−2222000000000000000000000000000000000000

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