Finite Group Databasebeta

← Group #348334

Character table — Group #348334

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442222224444444488888888224444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ511111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ811111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ91111111111111111-1-1-1-11111-1-1-1-11111111111-1-11-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-11111-1-1-1-11111111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-111-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-22-2-2-22000022-2-20000222222222200-200-2-2-2-2-200000000000000000000
χ182222222222-22-2-2-22000022-2-2000022-2-2-2-2-2-2-2-200-200-2222200000000000000000000
χ192222222222-22-2-2-220000-2-2-2-20000-2-22222-2-2-2-2002002-2-22200000000000000000000
χ202222222222-22-2-2-220000-2-2-2-20000-2-2-2-2-2-2222200200222-2-200000000000000000000
χ2122222222-2-22-2222-2222222-2-2-2-2-2-2-2-20000000022-2-2-22000000000000000000000000
χ2222222222-2-22-2222-22222-2-2-2-2-2-2-2-22200000000-2-2222-2000000000000000000000000
χ2322222222-2-22-2222-2-2-2-2-222-2-22222-2-200000000-2-2-2222000000000000000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2-2-222222200000000222-2-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022220000-2-20000000000200-200002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000022220000-2-20000000000200-20000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2220000220000000000-200200002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2220000220000000000-20020000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-2-22-22-20-2000200002-20000002-222-2-222-2-2000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ30222-2-2-22-22-20-2000200002-20000002-222-2-222-2-2000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ31222-2-2-22-22-20-2000200002-20000002-2-2-222-2-222000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ32222-2-2-22-22-20-2000200002-20000002-2-2-222-2-222000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ33222-2-2-22-22-20-200020000-22000000-2222-2-2-2-222000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ34222-2-2-22-22-20-200020000-22000000-2222-2-2-2-222000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ35222-2-2-22-22-20-200020000-22000000-22-2-22222-2-2000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ36222-2-2-22-22-20-200020000-22000000-22-2-22222-2-2000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ372-2-22-2-222222-2-2-22-222-2-2002-222-2-20000002i−2i2i−2i000000002i−2i00002i−2i2i−2i000000000000
χ382-2-22-2-222222-2-2-22-222-2-2002-222-2-2000000−2i2i−2i2i00000000−2i2i0000−2i2i−2i2i000000000000
χ392-2-22-2-222222-2-2-22-2-2-222002-2-2-2220000002i−2i2i−2i000000002i−2i0000−2i2i−2i2i000000000000
χ402-2-22-2-222222-2-2-22-2-2-222002-2-2-222000000−2i2i−2i2i00000000−2i2i00002i−2i2i−2i000000000000
χ412-2-22-2-22222-2-222-2-2000000-2200000000002i−2i2i−2i2-202-2000−2i2i2i−2i2i−2i0000000000000000
χ422-2-22-2-22222-2-222-2-2000000-2200000000002i−2i2i−2i-220-22000−2i2i−2i2i−2i2i0000000000000000
χ432-2-22-2-22222-2-222-2-2000000-220000000000−2i2i−2i2i2-202-20002i−2i−2i2i−2i2i0000000000000000
χ442-2-22-2-22222-2-222-2-2000000-220000000000−2i2i−2i2i-220-220002i−2i2i−2i2i−2i0000000000000000
χ452-2-22-2-222-2-222-2-22222-2-200-22-2-222002-22-200000000002-2002-2-220000000000000000
χ462-2-22-2-222-2-222-2-22222-2-200-22-2-22200-22-220000000000-2200-222-20000000000000000
χ472-2-22-2-222-2-222-2-222-2-22200-2222-2-2002-22-200000000002-200-222-20000000000000000
χ482-2-22-2-222-2-222-2-222-2-22200-2222-2-200-22-220000000000-22002-2-220000000000000000
χ492-2-22-2-222-2-2-2222-220000002-20000002-22-200002-20-220-220000002-2-22000000000000
χ502-2-22-2-222-2-2-2222-220000002-20000002-22-20000-2202-20-22000000-222-2000000000000
χ512-2-22-2-222-2-2-2222-220000002-2000000-22-2200002-20-2202-2000000-222-2000000000000
χ522-2-22-2-222-2-2-2222-220000002-2000000-22-220000-2202-202-20000002-2-22000000000000
χ53444-4-4-44-4-4404000-400004-4000000-4400000000000000000000000000000000000000
χ54444-4-4-44-4-4404000-40000-440000004-400000000000000000000000000000000000000
χ5544-4-44-4-4400404-4-40000000004i−4i4i−4i0000000000000000000000000000000000000000
χ5644-4-44-4-4400404-4-4000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ5744-4-44-4-4400-40-44404-44-4000000000000000000000000000000000000000000000000
χ5844-4-44-4-4400-40-4440-44-44000000000000000000000000000000000000000000000000
χ594-44-4-44-440040-44-40000000004i−4i−4i4i0000000000000000000000000000000000000000
χ604-44-4-44-440040-44-4000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ614-44-4-44-4400-404-4404-4-44000000000000000000000000000000000000000000000000
χ624-44-4-44-4400-404-440-444-4000000000000000000000000000000000000000000000000
χ634-4-4-4444-44-404000-40000000000000000004i−4i−4i4i000000000000000000000000000000
χ644-4-4-4444-44-404000-4000000000000000000−4i4i4i−4i000000000000000000000000000000
χ654-4-4-4444-4-440-40004000000000000004-4-440000000000000000000000000000000000
χ664-4-4-4444-4-440-4000400000000000000-444-40000000000000000000000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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