Finite Group Databasebeta

← Group #292576

Character table — Group #292576

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444444444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111111111111-1-1-1-111111-1-1-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-111111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111-11
χ111111111111111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-1-111-1-111-11
χ121111111111111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-111-1-111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1111-1
χ1722222222222-2-2-2-2222220000-2-2-2-2-2-200000022-2-20000000000000000-220000000000
χ1822222222222-2-2-2-2222220000-2-2-2-2-2-2000000-2-22200000000000000002-20000000000
χ1922222222222-2-2-2-22-2-2-2-20000-22222-200000022220000000000000000-2-20000000000
χ2022222222222-2-2-2-22-2-2-2-20000-22222-2000000-2-2-2-20000000000000000220000000000
χ2122222222-2-2-22222-222-2-22222-2-2-222-2-2-2-2-22200000000000000000000000000000000
χ2222222222-2-2-22222-222-2-2-2-2-2-2-2-2-222-22222-2-200000000000000000000000000000000
χ2322222222-2-2-22222-2-2-2222222-222-2-2-222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-22222-2-2-222-2-2-2-2-222-2-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-20000222-2-2200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-20000222-2-220000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22200002-2-222200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22200002-2-22220000000000000000000000000000-222-2000000
χ2922-2-22-22-20002-22-20002i−2i2i2i−2i−2i02i−2i0002-200000000i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000
χ3022-2-22-22-20002-22-20002i−2i2i2i−2i−2i02i−2i0002-200000000−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000
χ3122-2-22-22-20002-22-20002i−2i−2i−2i2i2i02i−2i000-2200000000i2i2−i2−i222−2−2−2−222−i2−i2i2i2000000000000
χ3222-2-22-22-20002-22-20002i−2i−2i−2i2i2i02i−2i000-2200000000−i2−i2i2i2−2−22222−2−2i2i2−i2−i2000000000000
χ3322-2-22-22-20002-22-2000−2i2i2i2i−2i−2i0−2i2i000-2200000000i2i2−i2−i2−2−22222−2−2−i2−i2i2i2000000000000
χ3422-2-22-22-20002-22-2000−2i2i2i2i−2i−2i0−2i2i000-2200000000−i2−i2i2i222−2−2−2−222i2i2−i2−i2000000000000
χ3522-2-22-22-20002-22-2000−2i2i−2i−2i2i2i0−2i2i0002-200000000i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000
χ3622-2-22-22-20002-22-2000−2i2i−2i−2i2i2i0−2i2i0002-200000000−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000
χ372-22-2-222-222-22-2-22-200002i−2i2i−2i-200002002i−2i00000000002i−2i2i−2i00002-22-2000000000000
χ382-22-2-222-222-22-2-22-200002i−2i2i−2i-200002002i−2i0000000000−2i2i−2i2i0000-22-22000000000000
χ392-22-2-222-222-22-2-22-20000−2i2i−2i2i-20000200−2i2i00000000002i−2i2i−2i0000-22-22000000000000
χ402-22-2-222-222-22-2-22-20000−2i2i−2i2i-20000200−2i2i0000000000−2i2i−2i2i00002-22-2000000000000
χ412-22-2-222-2-2-222-2-22200002i−2i2i−2i20000-200−2i2i0000002-22-200002i−2i2i−2i0000000000000000
χ422-22-2-222-2-2-222-2-22200002i−2i2i−2i20000-200−2i2i000000-22-220000−2i2i−2i2i0000000000000000
χ432-22-2-222-2-2-222-2-2220000−2i2i−2i2i20000-2002i−2i0000002-22-20000−2i2i−2i2i0000000000000000
χ442-22-2-222-2-2-222-2-2220000−2i2i−2i2i20000-2002i−2i000000-22-2200002i−2i2i−2i0000000000000000
χ452-2-22-2-22200022-2-202-2002-2-220002-2000002-20000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ462-2-22-2-22200022-2-202-2002-2-220002-2000002-20000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ472-2-22-2-22200022-2-202-200-222-20002-200000-220000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ482-2-22-2-22200022-2-202-200-222-20002-200000-220000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ492-2-22-2-22200022-2-20-22002-2-22000-2200000-220000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ502-2-22-2-22200022-2-20-22002-2-22000-2200000-220000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ512-2-22-2-22200022-2-20-2200-222-2000-22000002-20000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ522-2-22-2-22200022-2-20-2200-222-2000-22000002-20000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ53444-4-4-4-444-440000-400000000000000000000004-40000000000000000000000000000
χ54444-4-4-4-444-440000-40000000000000000000000-440000000000000000000000000000
χ55444-4-4-4-44-44-400004000000000000000000004i−4i000000000000000000000000000000
χ56444-4-4-4-44-44-40000400000000000000000000−4i4i000000000000000000000000000000
χ5744-4-44-44-4000-44-440004i−4i00000−4i4i00000000000000000000000000000000000000000
χ5844-4-44-44-4000-44-44000−4i4i000004i−4i00000000000000000000000000000000000000000
χ594-4444-4-4-44-4-40000400000000000000000000000000000000000000000000002i2−2i20000
χ604-4444-4-4-44-4-4000040000000000000000000000000000000000000000000000−2i22i20000
χ614-4444-4-4-4-4440000-400000000000000000000000000000000000000000000000022−2200
χ624-4444-4-4-4-4440000-4000000000000000000000000000000000000000000000000−222200
χ634-44-4-444-444-4-444-4-40000000040000-400000000000000000000000000000000000000
χ644-44-4-444-4-4-44-444-4400000000-40000400000000000000000000000000000000000000
χ654-4-44-4-444000-4-44404-4000000000-44000000000000000000000000000000000000000
χ664-4-44-4-444000-4-4440-440000000004-4000000000000000000000000000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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