Finite Group Databasebeta

← Group #292619

Character table — Group #292619

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444444444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ6111111111111111111111-1-1-1-111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1
χ7111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1111111-1-1
χ8111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-111
χ91111111111111111-1-11-1-11111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-11-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-11
χ111111111111111111-1-11-1-11111-1-1-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-1-1-111-1-111-11
χ121111111111111111-1-11-1-11111-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-11111-1-11-1
χ131111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ141111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-11
χ151111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-11
χ161111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1111-1
χ172222222222-2-222-2-222-2-2-2222222-2-2-22200-2-2-2-2000000000000000000000000000000
χ182222222222-2-222-2-222-2-2-2-2-2-2-222-2-2-2-2-2002222000000000000000000000000000000
χ192222222222-2-222-2-2-2-2-2222222-2-222-2-2-200-2-222000000000000000000000000000000
χ202222222222-2-222-2-2-2-2-222-2-2-2-2-2-222-2220022-2-2000000000000000000000000000000
χ2122222222-2-222-2-22222-2-2-20000-2-222-200220000220000000000000000-200-200000000
χ2222222222-2-222-2-22222-2-2-20000-2-222-200-2-20000-2-20000000000000000200200000000
χ2322222222-2-222-2-222-2-2-222000022-2-2-200220000-2-20000000000000000200-200000000
χ2422222222-2-222-2-222-2-2-222000022-2-2-200-2-20000220000000000000000-200200000000
χ2522222222-2-2-2-2-2-2-2-2222220000-2-2-2-220000000000000000000000000002-202-2000000
χ2622222222-2-2-2-2-2-2-2-2222220000-2-2-2-22000000000000000000000000000-220-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22-2-20000222220000000000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22-2-2000022222000000000000000000000000000-2202-2000000
χ29222-22-2-2-2-2-20022002-200022-2-22-20002-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ30222-22-2-2-2-2-20022002-200022-2-22-20002-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ31222-22-2-2-2-2-20022002-2000-2-2222-2000-2200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ32222-22-2-2-2-2-20022002-2000-2-2222-2000-2200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ33222-22-2-2-2-2-2002200-2200022-2-2-22000-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ34222-22-2-2-2-2-2002200-2200022-2-2-22000-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ35222-22-2-2-2-2-2002200-22000-2-222-220002-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-22-2-2-2-2-2002200-22000-2-222-220002-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ372-2-222-2-222-2222-2-2-200-2002i−2i2i−2i0000200002i−2i00002i−2i2i−2i00002-22-20000000000000000
χ382-2-222-2-222-2222-2-2-200-2002i−2i2i−2i0000200002i−2i0000−2i2i−2i2i0000-22-220000000000000000
χ392-2-222-2-222-2222-2-2-200-200−2i2i−2i2i000020000−2i2i00002i−2i2i−2i0000-22-220000000000000000
χ402-2-222-2-222-2222-2-2-200-200−2i2i−2i2i000020000−2i2i0000−2i2i−2i2i00002-22-20000000000000000
χ412-2-222-2-222-2-2-22-222002002i−2i2i−2i0000-20000−2i2i000000002-22-200002i−2i2i−2i000000000000
χ422-2-222-2-222-2-2-22-222002002i−2i2i−2i0000-20000−2i2i00000000-22-220000−2i2i−2i2i000000000000
χ432-2-222-2-222-2-2-22-22200200−2i2i−2i2i0000-200002i−2i000000002-22-20000−2i2i−2i2i000000000000
χ442-2-222-2-222-2-2-22-22200200−2i2i−2i2i0000-200002i−2i00000000-22-2200002i−2i2i−2i000000000000
χ452-2-2-2222-2-22002-2000002i−2i2i−2i−2i2i002i−2i00000002-2002−2−22i2−i2−i2i2−i2i2i2−i2−222−2000000000000
χ462-2-2-2222-2-22002-2000002i−2i2i−2i−2i2i002i−2i00000002-200−222−2−i2i2i2−i2i2−i2−i2i22−2−22000000000000
χ472-2-2-2222-2-22002-2000002i−2i−2i2i2i−2i002i−2i0000000-22002−2−22i2−i2−i2i2i2−i2−i2i22−2−22000000000000
χ482-2-2-2222-2-22002-2000002i−2i−2i2i2i−2i002i−2i0000000-2200−222−2−i2i2i2−i2−i2i2i2−i2−222−2000000000000
χ492-2-2-2222-2-22002-200000−2i2i2i−2i−2i2i00−2i2i0000000-22002−2−22−i2i2i2−i2−i2i2i2−i22−2−22000000000000
χ502-2-2-2222-2-22002-200000−2i2i2i−2i−2i2i00−2i2i0000000-2200−222−2i2−i2−i2i2i2−i2−i2i2−222−2000000000000
χ512-2-2-2222-2-22002-200000−2i2i−2i2i2i−2i00−2i2i00000002-2002−2−22−i2i2i2−i2i2−i2−i2i2−222−2000000000000
χ522-2-2-2222-2-22002-200000−2i2i−2i2i2i−2i00−2i2i00000002-200−222−2i2−i2−i2i2−i2i2i2−i22−2−22000000000000
χ53444-44-4-4-44400-4-4004-40000000-4400000000000000000000000000000000000000000
χ54444-44-4-4-44400-4-400-4400000004-400000000000000000000000000000000000000000
χ5544-4-4-44-44004-4004-400000000000000000000000000000000000000000000002i2−2i20000
χ5644-4-4-44-44004-4004-40000000000000000000000000000000000000000000000−2i22i20000
χ5744-4-4-44-4400-4400-440000000000000000000000000000000000000000000000002i2−2i200
χ5844-4-4-44-4400-4400-44000000000000000000000000000000000000000000000000−2i22i200
χ594-44-4-4-444004-400-4400000000000000004i−4i0000000000000000000000000000000000
χ604-44-4-4-444004-400-440000000000000000−4i4i0000000000000000000000000000000000
χ614-44-4-4-44400-44004-400000000000000000000004i−4i0000000000000000000000000000
χ624-44-4-4-44400-44004-40000000000000000000000−4i4i0000000000000000000000000000
χ634-4-444-4-44-4444-44-4-40040000000000-400000000000000000000000000000000000000
χ644-4-444-4-44-44-4-4-444400-40000000000400000000000000000000000000000000000000
χ654-4-4-4444-44-400-44000004i−4i000000−4i4i000000000000000000000000000000000000000
χ664-4-4-4444-44-400-4400000−4i4i0000004i−4i000000000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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