Finite Group Databasebeta

← Group #324461

Character table — Group #324461

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888822444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111111111111111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-11
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-11-1-11
χ172222222222-2-2-222-222-2-2220000000022-2-2-2-2-2-2220000000000000000000000000000
χ182222222222-2-2-222-222-2-22200000000-2-2-2-22222-2-20000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-2000000002222-2-222-2-20000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-200000000-2-22222-2-2220000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-22222-2-2-2-2002-200000022-2-2000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-2-22222002-2000000-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2222222-2-2-2-200-22000000-2-222000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-222-2-2-2-2222200-2200000022-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000000000-220000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000000000-22000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200000000002-20000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000002-2000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2922-2-2-2-22222000-2-202-2002-222−2−222−2−200002i−2i2i−2i002−22−200000000i2−i2i2−i2i2−i2i2−i200000000
χ3022-2-2-2-22222000-2-202-2002-222−2−222−2−20000−2i2i−2i2i002−22−200000000−i2i2−i2i2−i2i2−i2i200000000
χ3122-2-2-2-22222000-2-202-2002-2−2−222−2−22200002i−2i2i−2i00−22−2200000000−i2i2−i2i2−i2i2−i2i200000000
χ3222-2-2-2-22222000-2-202-2002-2−2−222−2−2220000−2i2i−2i2i00−22−2200000000i2−i2i2−i2i2−i2i2−i200000000
χ3322-2-2-2-22222000-2-20-2200-2222−2−222−2−200002i−2i−2i2i00−22−2200000000i2−i2i2−i2−i2i2−i2i200000000
χ3422-2-2-2-22222000-2-20-2200-2222−2−222−2−20000−2i2i2i−2i00−22−2200000000−i2i2−i2i2i2−i2i2−i200000000
χ3522-2-2-2-22222000-2-20-2200-22−2−222−2−22200002i−2i−2i2i002−22−200000000−i2i2−i2i2i2−i2i2−i200000000
χ3622-2-2-2-22222000-2-20-2200-22−2−222−2−2220000−2i2i2i−2i002−22−200000000i2−i2i2−i2−i2i2−i2i200000000
χ3722-2-2-2-222-2-20002202-200-2222−2−2−2−2222-20000002-22−2−22000000002−2−222−2−2200000000
χ3822-2-2-2-222-2-20002202-200-2222−2−2−2−222-22000000-222−2−2200000000−222−2−222−200000000
χ3922-2-2-2-222-2-20002202-200-22−2−22222−2−22-20000002-2−222−200000000−222−2−222−200000000
χ4022-2-2-2-222-2-20002202-200-22−2−22222−2−2-22000000-22−222−2000000002−2−222−2−2200000000
χ4122-2-2-2-222-2-2000220-22002-222−2−2−2−2222-2000000-22−222−2000000002−2−22−222−200000000
χ4222-2-2-2-222-2-2000220-22002-222−2−2−2−222-220000002-2−222−200000000−222−22−2−2200000000
χ4322-2-2-2-222-2-2000220-22002-2−2−22222−2−22-2000000-222−2−2200000000−222−22−2−2200000000
χ4422-2-2-2-222-2-2000220-22002-2−2−22222−2−2-220000002-22−2−22000000002−2−22−222−200000000
χ452-2-2-2222-22-222-22-2-2002-2002i−2i2i−2i2i−2i2i−2i00000000000000000022-2-200000000002i−2i0000
χ462-2-2-2222-22-222-22-2-2002-2002i−2i2i−2i2i−2i2i−2i000000000000000000-2-2220000000000−2i2i0000
χ472-2-2-2222-22-222-22-2-2002-200−2i2i−2i2i−2i2i−2i2i00000000000000000022-2-20000000000−2i2i0000
χ482-2-2-2222-22-222-22-2-2002-200−2i2i−2i2i−2i2i−2i2i000000000000000000-2-22200000000002i−2i0000
χ492-2-2-2222-2-2222-2-22-200-22002i−2i2i−2i−2i2i−2i2i0000000000000022-2-20000000000002i−2i000000
χ502-2-2-2222-2-2222-2-22-200-22002i−2i2i−2i−2i2i−2i2i00000000000000-2-222000000000000−2i2i000000
χ512-2-2-2222-2-2222-2-22-200-2200−2i2i−2i2i2i−2i2i−2i0000000000000022-2-2000000000000−2i2i000000
χ522-2-2-2222-2-2222-2-22-200-2200−2i2i−2i2i2i−2i2i−2i00000000000000-2-2220000000000002i−2i000000
χ53444-44-4-4-4004-4400-4000000000000000000000000000022−2222−2200000000000000000000
χ54444-44-4-4-4004-4400-40000000000000000000000000000−2222−222200000000000000000000
χ55444-44-4-4-400-44-4004000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ56444-44-4-4-400-44-400400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ574-444-4-44-44-4000-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ584-444-4-44-44-4000-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-444-4-44-4-440004-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ604-444-4-44-4-440004-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-444-4-44004-4-4004000000000000000000000000000022−22−222200000000000000000000
χ624-4-444-4-44004-4-40040000000000000000000000000000−222222−2200000000000000000000
χ634-4-444-4-4400-44400-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ644-4-444-4-4400-44400-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ654-4-4-4444-44-4-4-444-4400-44000000000000000000000000000000000000000000000000
χ664-4-4-4444-4-44-4-44-444004-4000000000000000000000000000000000000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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