Finite Group Databasebeta

← Group #292559

Character table — Group #292559

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
χ3111111111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ611111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1111111-1-1
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-111
χ91111111111111111-1-1-1-11111-1-11-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-11111-1-11-1-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-11
χ111111111111111111-1-1-1-11111-1-11-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-111-11
χ121111111111111111-1-1-1-11111-1-11-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1111-1
χ172222222222-2-222-2-222220000-2-2-2-2-2-222002200000000000000000000-200-200000000
χ182222222222-2-222-2-222220000-2-2-2-2-2-2-2-200-2-200000000000000000000200200000000
χ192222222222-2-222-2-2-2-2-2-2000022-222-22200-2-200000000000000000000200-200000000
χ202222222222-2-222-2-2-2-2-2-2000022-222-2-2-2002200000000000000000000-200200000000
χ2122222222-2-222-2-22222-2-2222222-2-2-2-2002200-2-2-2-20000000000000000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-222-2-2-2-200-2-20022220000000000000000000000000000
χ2322222222-2-222-2-222-2-2222222-2-2-222-200-2-200-2-2220000000000000000000000000000
χ2422222222-2-222-2-222-2-222-2-2-2-2-2-2-222-200220022-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-20000-2-222220000000000000000000000000002-202-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-20000-2-22222000000000000000000000000000-220-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2220000222-2-220000000000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2220000222-2-22000000000000000000000000000-2202-2000000
χ2922-2-2-22-22002-2002-2002i−2i2i2i−2i−2i0002i−2i0000000002-2i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000
χ3022-2-2-22-22002-2002-2002i−2i2i2i−2i−2i0002i−2i0000000002-2−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000
χ3122-2-2-22-22002-2002-2002i−2i−2i−2i2i2i0002i−2i000000000-22i2i2−i2−i222−2−2−2−222−i2−i2i2i2000000000000
χ3222-2-2-22-22002-2002-2002i−2i−2i−2i2i2i0002i−2i000000000-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i2000000000000
χ3322-2-2-22-22002-2002-200−2i2i2i2i−2i−2i000−2i2i000000000-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i2000000000000
χ3422-2-2-22-22002-2002-200−2i2i2i2i−2i−2i000−2i2i000000000-22−i2−i2i2i222−2−2−2−222i2i2−i2−i2000000000000
χ3522-2-2-22-22002-2002-200−2i2i−2i−2i2i2i000−2i2i0000000002-2i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000
χ3622-2-2-22-22002-2002-200−2i2i−2i−2i2i2i000−2i2i0000000002-2−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000
χ372-222-22-2-200-2-200222-2002-22-22-20000002-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-222-22-2-200-2-200222-2002-22-22-20000002-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ392-222-22-2-200-2-200222-200-22-222-2000000-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-222-22-2-200-2-200222-200-22-222-2000000-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ412-222-22-2-200-2-20022-22002-22-2-22000000-22000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ422-222-22-2-200-2-20022-22002-22-2-22000000-22000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ432-222-22-2-200-2-20022-2200-22-22-220000002-2000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ442-222-22-2-200-2-20022-2200-22-22-220000002-2000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-2-2222-222-22-2-22-200002i−2i−2i2i00-20020000002i−2i0000002i−2i−2i2i0000-222-2000000000000
χ462-2-2-2222-222-22-2-22-200002i−2i−2i2i00-20020000002i−2i000000−2i2i2i−2i00002-2-22000000000000
χ472-2-2-2222-222-22-2-22-20000−2i2i2i−2i00-2002000000−2i2i0000002i−2i−2i2i00002-2-22000000000000
χ482-2-2-2222-222-22-2-22-20000−2i2i2i−2i00-2002000000−2i2i000000−2i2i2i−2i0000-222-2000000000000
χ492-2-2-2222-2-2-2-22222-200002i−2i−2i2i00200-2000000−2i2i002-2-220000−2i2i2i−2i0000000000000000
χ502-2-2-2222-2-2-2-22222-200002i−2i−2i2i00200-2000000−2i2i00-222-200002i−2i−2i2i0000000000000000
χ512-2-2-2222-2-2-2-22222-20000−2i2i2i−2i00200-20000002i−2i002-2-2200002i−2i−2i2i0000000000000000
χ522-2-2-2222-2-2-2-22222-20000−2i2i2i−2i00200-20000002i−2i00-222-20000−2i2i2i−2i0000000000000000
χ53444-44-4-4-44-4004-4000000000000000000004-400000000000000000000000000000000
χ54444-44-4-4-44-4004-400000000000000000000-4400000000000000000000000000000000
χ55444-44-4-4-4-4400-4400000000000000004-4000000000000000000000000000000000000
χ56444-44-4-4-4-4400-440000000000000000-44000000000000000000000000000000000000
χ5744-4-4-44-4400-4400-44004i−4i0000000−4i4i000000000000000000000000000000000000000
χ5844-4-4-44-4400-4400-4400−4i4i00000004i−4i000000000000000000000000000000000000000
χ594-444-44-4-4004400-4-44-4000000-44000000000000000000000000000000000000000000
χ604-444-44-4-4004400-4-4-440000004-4000000000000000000000000000000000000000000
χ614-4-444-4-444-400-440000000000000000000000000000000000000000000000002i2−2i20000
χ624-4-444-4-444-400-44000000000000000000000000000000000000000000000000−2i22i20000
χ634-4-444-4-44-44004-4000000000000000000000000000000000000000000000000002i2−2i200
χ644-4-444-4-44-44004-400000000000000000000000000000000000000000000000000−2i22i200
χ654-4-4-4444-4444-4-4-4-440000000000400-400000000000000000000000000000000000000
χ664-4-4-4444-4-4-44-444-440000000000-400400000000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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