Finite Group Databasebeta

← Group #271069

Character table — Group #271069

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444422222244448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111111111111-1-11-1-1-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-11111-1-11-1
χ101111111111111111-1-11-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-111-11
χ111111111111111111-1-11-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-111-11
χ121111111111111111-1-11-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-111-1-11-1
χ131111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-1111-1
χ141111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-11
χ151111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-11
χ161111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-111111111-1-1-1-11-1-1-111-1-1111-1
χ172222222222-2-222-2-222-2-2-222-2-22222-2-2-2-2-20000220000000000000000000000000000
χ182222222222-2-222-2-222-2-2-222-2-2-2-2-2-2-222220000-2-20000000000000000000000000000
χ192222222222-2-222-2-2-2-2-222-2-2222222-2-2-2220000-2-20000000000000000000000000000
χ202222222222-2-222-2-2-2-2-222-2-222-2-2-2-2-222-2-20000220000000000000000000000000000
χ2122222222-2-222-2-22222-2-2-2-2-2220000-200002222000000000000000000-2-20000000000
χ2222222222-2-222-2-22222-2-2-2-2-2220000-20000-2-2-2-2000000000000000000220000000000
χ2322222222-2-222-2-222-2-2-22222-2-20000-2000022-2-20000000000000000002-20000000000
χ2422222222-2-222-2-222-2-2-22222-2-20000-20000-2-222000000000000000000-220000000000
χ2522222222-2-2-2-2-2-2-2-222222-2-2-2-20000200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222222-2-2-2-2000020000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22-2-222220000200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22-2-22222000020000000000000000000000000000-222-2000000
χ29222-22-2-2-2-2-20022002-20002-2002i2i−2i−2i0000000002i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ30222-22-2-2-2-2-20022002-20002-2002i2i−2i−2i0000000002i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ31222-22-2-2-2-2-20022002-20002-200−2i−2i2i2i000000000−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ32222-22-2-2-2-2-20022002-20002-200−2i−2i2i2i000000000−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ33222-22-2-2-2-2-2002200-22000-22002i2i−2i−2i000000000−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ34222-22-2-2-2-2-2002200-22000-22002i2i−2i−2i000000000−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ35222-22-2-2-2-2-2002200-22000-2200−2i−2i2i2i0000000002i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ36222-22-2-2-2-2-2002200-22000-2200−2i−2i2i2i0000000002i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ372-2-222-2-222-2222-2-2-20020000002-22-2-22-2000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ382-2-222-2-222-2222-2-2-20020000002-22-2-22-200000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ392-2-222-2-222-2222-2-2-2002000000-22-22-2-22000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ402-2-222-2-222-2222-2-2-2002000000-22-22-2-2200000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ412-2-222-2-222-2-2-22-22200-20000002-22-22-220000000000002-22-200002-22-2000000000000
χ422-2-222-2-222-2-2-22-22200-20000002-22-22-22000000000000-22-220000-22-22000000000000
χ432-2-222-2-222-2-2-22-22200-2000000-22-2222-20000000000002-22-20000-22-22000000000000
χ442-2-222-2-222-2-2-22-22200-2000000-22-2222-2000000000000-22-2200002-22-2000000000000
χ452-2-2-2222-2-22002-2000002i−2i002i−2i2i−2i−2i2i0002-20000002−2−22i2−i2−i2i2−i2i2i2−i22−2−22000000000000
χ462-2-2-2222-2-22002-2000002i−2i002i−2i2i−2i−2i2i0002-2000000−222−2−i2i2i2−i2i2−i2−i2i2−222−2000000000000
χ472-2-2-2222-2-22002-2000002i−2i002i−2i−2i2i2i−2i000-220000002−2−22i2−i2−i2i2i2−i2−i2i2−222−2000000000000
χ482-2-2-2222-2-22002-2000002i−2i002i−2i−2i2i2i−2i000-22000000−222−2−i2i2i2−i2−i2i2i2−i22−2−22000000000000
χ492-2-2-2222-2-22002-200000−2i2i00−2i2i2i−2i−2i2i000-220000002−2−22−i2i2i2−i2−i2i2i2−i2−222−2000000000000
χ502-2-2-2222-2-22002-200000−2i2i00−2i2i2i−2i−2i2i000-22000000−222−2i2−i2−i2i2i2−i2−i2i22−2−22000000000000
χ512-2-2-2222-2-22002-200000−2i2i00−2i2i−2i2i2i−2i0002-20000002−2−22−i2i2i2−i2i2−i2−i2i22−2−22000000000000
χ522-2-2-2222-2-22002-200000−2i2i00−2i2i−2i2i2i−2i0002-2000000−222−2i2−i2−i2i2−i2i2i2−i2−222−2000000000000
χ53444-44-4-4-44400-4-4004-4000-44000000000000000000000000000000000000000000000
χ54444-44-4-4-44400-4-400-440004-4000000000000000000000000000000000000000000000
χ5544-4-4-44-44004-4004-4000000000000000000000000000000000000000000000022−220000
χ5644-4-4-44-44004-4004-40000000000000000000000000000000000000000000000−22220000
χ5744-4-4-44-4400-4400-4400000000000000000000000000000000000000000000000022−2200
χ5844-4-4-44-4400-4400-44000000000000000000000000000000000000000000000000−222200
χ594-44-4-4-444004-400-440000000000000000004-400000000000000000000000000000000
χ604-44-4-4-444004-400-44000000000000000000-4400000000000000000000000000000000
χ614-44-4-4-44400-44004-4000000000000000000004-4000000000000000000000000000000
χ624-44-4-4-44400-44004-400000000000000000000-44000000000000000000000000000000
χ634-4-444-4-44-4444-44-4-400-40000000000400000000000000000000000000000000000000
χ644-4-444-4-44-44-4-4-44440040000000000-400000000000000000000000000000000000000
χ654-4-4-4444-44-400-44000004i−4i00−4i4i0000000000000000000000000000000000000000000
χ664-4-4-4444-44-400-4400000−4i4i004i−4i0000000000000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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