Finite Group Databasebeta

← Group #278950

Character table — Group #278950

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444442244448888888844444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-1
χ91111111111111111-1-111-1-111111111-111-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-111-1-111111111-111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ121111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-11-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-11-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1111-11-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-11-11
χ17222222222-2-2-2222-222-2-2-2-22222-2-2-2-2200-2000000-2-200002200000000000000000000
χ18222222222-2-2-2222-222-2-2-2-2-2-2-2-22222200-2000000220000-2-200000000000000000000
χ19222222222-2-2-2222-2-2-2-2-2222222-2-2-2-2-2002000000220000-2-200000000000000000000
χ20222222222-2-2-2222-2-2-2-2-222-2-2-2-22222-2002000000-2-200002200000000000000000000
χ2122222222-2222-2-2-2222-2-22200000000-222-222-2-2-2-20000000000000000000000000000
χ2222222222-2222-2-2-2222-2-22200000000-2-2-2-2-2-222220000000000000000000000000000
χ2322222222-2222-2-2-22-2-2-2-2-2-2000000002222-2-222-2-20000000000000000000000000000
χ2422222222-2222-2-2-22-2-2-2-2-2-2000000002-2-2222-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-2002000000002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-200200000000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200000000200-2000000002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000200-200000000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2922-2-2-2-222022-2000-22-2002-222−2−222−2−202i−2i02i−2i00002−2i2−i2i2−i22−2i2−i2i2−i20000000000000000
χ3022-2-2-2-222022-2000-22-2002-222−2−222−2−20−2i2i0−2i2i00002−2−i2i2−i2i22−2−i2i2−i2i20000000000000000
χ3122-2-2-2-222022-2000-22-2002-2−2−222−2−22202i−2i02i−2i0000−22−i2i2−i2i2−22−i2i2−i2i20000000000000000
χ3222-2-2-2-222022-2000-22-2002-2−2−222−2−2220−2i2i0−2i2i0000−22i2−i2i2−i2−22i2−i2i2−i20000000000000000
χ3322-2-2-2-222022-2000-2-2200-2222−2−222−2−202i−2i0−2i2i0000−22i2−i2i2−i2−22−i2i2−i2i20000000000000000
χ3422-2-2-2-222022-2000-2-2200-2222−2−222−2−20−2i2i02i−2i0000−22−i2i2−i2i2−22i2−i2i2−i20000000000000000
χ3522-2-2-2-222022-2000-2-2200-22−2−222−2−22202i−2i0−2i2i00002−2−i2i2−i2i22−2i2−i2i2−i20000000000000000
χ3622-2-2-2-222022-2000-2-2200-22−2−222−2−2220−2i2i02i−2i00002−2i2−i2i2−i22−2−i2i2−i2i20000000000000000
χ3722-2-2-2-2220-2-2200022-200-2222−2−2−2−2220000002-22-2−222−2−222−22−2−220000000000000000
χ3822-2-2-2-2220-2-2200022-200-2222−2−2−2−222000000-22-22−22−222−22−2−222−20000000000000000
χ3922-2-2-2-2220-2-2200022-200-22−2−22222−2−20000002-22-22−2−222−2−22−222−20000000000000000
χ4022-2-2-2-2220-2-2200022-200-22−2−22222−2−2000000-22-222−22−2−22−222−2−220000000000000000
χ4122-2-2-2-2220-2-220002-22002-222−2−2−2−2220000002-2-222−2−222−2−222−2−220000000000000000
χ4222-2-2-2-2220-2-220002-22002-222−2−2−2−222000000-222-22−22−2−22−22−222−20000000000000000
χ4322-2-2-2-2220-2-220002-22002-2−2−22222−2−20000002-2-22−222−2−222−2−222−20000000000000000
χ4422-2-2-2-2220-2-220002-22002-2−2−22222−2−2000000-222-2−22−222−22−22−2−220000000000000000
χ452-2-22-222-2-22-222-22-2002-2002-22-22-22-200000000000000000000002i2i−2i−2i00002i−2i000000
χ462-2-22-222-2-22-222-22-2002-2002-22-22-22-20000000000000000000000−2i−2i2i2i0000−2i2i000000
χ472-2-22-222-2-22-222-22-2002-200-22-22-22-2200000000000000000000002i2i−2i−2i0000−2i2i000000
χ482-2-22-222-2-22-222-22-2002-200-22-22-22-220000000000000000000000−2i−2i2i2i00002i−2i000000
χ492-2-22-222-2-2-22-22-22200-22002-22-2-22-220000000000000000000000000022-2-2002-20000
χ502-2-22-222-2-2-22-22-22200-22002-22-2-22-2200000000000000000000000000-2-22200-220000
χ512-2-22-222-2-2-22-22-22200-2200-22-222-22-20000000000000000000000000022-2-200-220000
χ522-2-22-222-2-2-22-22-22200-2200-22-222-22-200000000000000000000000000-2-222002-20000
χ534444-4-4-4-44000-4-440000000000000000000000000000000000000000022−2222−2200000000
χ544444-4-4-4-44000-4-4400000000000000000000000000000000000000000−2222−222200000000
χ554444-4-4-4-4-400044-4000000000000000000000000000000000000022−2222−22000000000000
χ564444-4-4-4-4-400044-40000000000000000000000000000000000000−2222−2222000000000000
χ574-44-44-44-404-4-4000400000022−22−222222−22−222200000000000000000000000000000000000000
χ584-44-44-44-404-4-40004000000−222222−22−222222−2200000000000000000000000000000000000000
χ594-44-44-44-40-444000-400000022−22−2222−222222−2200000000000000000000000000000000000000
χ604-44-44-44-40-444000-4000000−222222−2222−22−222200000000000000000000000000000000000000
χ614-4-444-4-4440004-4-400000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ624-4-444-4-4440004-4-40000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ634-4-444-4-44-4000-4440000000000000000000000000000000000000000022−22−222200000000
χ644-4-444-4-44-4000-44400000000000000000000000000000000000000000−222222−2200000000
χ654-4-44-444-444-44-44-4-400-44000000000000000000000000000000000000000000000000
χ664-4-44-444-44-44-4-44-44004-4000000000000000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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