Finite Group Databasebeta

← Group #324481

Character table — Group #324481

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888822444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ91111111111111111-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111111111111111-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11
χ111111111111111111-1-111-1-111111111-1-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-11
χ121111111111111111-1-111-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-11-1-11
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-111-1
χ172222222222-2-2-222-222-2-2220000000022-222-2-2-2-2-20000000000000000000000000000
χ182222222222-2-2-222-222-2-22200000000-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000222-2-22-2-2220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-200000000-2-2222222-2-20000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-22222-2-2-2-200200-2000022-2-2000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-2-2222200200-20000-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2222222-2-2-2-200-20020000-2-222000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-222-2-2-2-2222200-2002000022-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000000000-200200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000000000-20020000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000000200-200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000000200-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2922-2-22-22-22-20002-202i−2i002i−2ii2i2−i2−i2i2i2−i2−i20000002i−2i2-22−22−2000000002−22−2i2−i2i2−i200000000
χ3022-2-22-22-22-20002-202i−2i002i−2ii2i2−i2−i2i2i2−i2−i2000000−2i2i-222−22−200000000−22−22−i2i2−i2i200000000
χ3122-2-22-22-22-20002-202i−2i002i−2i−i2−i2i2i2−i2−i2i2i20000002i−2i2-2−22−2200000000−22−22−i2i2−i2i200000000
χ3222-2-22-22-22-20002-202i−2i002i−2i−i2−i2i2i2−i2−i2i2i2000000−2i2i-22−22−22000000002−22−2i2−i2i2−i200000000
χ3322-2-22-22-22-20002-20−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i20000002i−2i-22−22−22000000002−22−2−i2i2−i2i200000000
χ3422-2-22-22-22-20002-20−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i2000000−2i2i2-2−22−2200000000−22−22i2−i2i2−i200000000
χ3522-2-22-22-22-20002-20−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i20000002i−2i-222−22−200000000−22−22i2−i2i2−i200000000
χ3622-2-22-22-22-20002-20−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i2000000−2i2i2-22−22−2000000002−22−2−i2i2−i2i200000000
χ3722-2-22-22-2-22000-2202i−2i00−2i2ii2i2−i2−i2−i2−i2i2i22-202i−2i000002−2−2200000000i2−i2−i2i2−222−200000000
χ3822-2-22-22-2-22000-2202i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2-220−2i2i000002−2−2200000000−i2i2i2−i22−2−2200000000
χ3922-2-22-22-2-22000-2202i−2i00−2i2i−i2−i2i2i2i2i2−i2−i22-202i−2i00000−222−200000000−i2i2i2−i22−2−2200000000
χ4022-2-22-22-2-22000-2202i−2i00−2i2i−i2−i2i2i2i2i2−i2−i2-220−2i2i00000−222−200000000i2−i2−i2i2−222−200000000
χ4122-2-22-22-2-22000-220−2i2i002i−2ii2i2−i2−i2−i2−i2i2i22-20−2i2i00000−222−200000000i2−i2−i2i22−2−2200000000
χ4222-2-22-22-2-22000-220−2i2i002i−2ii2i2−i2−i2−i2−i2i2i2-2202i−2i00000−222−200000000−i2i2i2−i2−222−200000000
χ4322-2-22-22-2-22000-220−2i2i002i−2i−i2−i2i2i2i2i2−i2−i22-20−2i2i000002−2−2200000000−i2i2i2−i2−222−200000000
χ4422-2-22-22-2-22000-220−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2-2202i−2i000002−2−2200000000i2−i2−i2i22−2−2200000000
χ452-2-22-2-2222-222-2-22-2002-2002i−2i2i−2i2i−2i2i−2i00000000000000000022-2-200000000002i−2i0000
χ462-2-22-2-2222-222-2-22-2002-2002i−2i2i−2i2i−2i2i−2i000000000000000000-2-2220000000000−2i2i0000
χ472-2-22-2-2222-222-2-22-2002-200−2i2i−2i2i−2i2i−2i2i00000000000000000022-2-20000000000−2i2i0000
χ482-2-22-2-2222-222-2-22-2002-200−2i2i−2i2i−2i2i−2i2i000000000000000000-2-22200000000002i−2i0000
χ492-2-22-2-222-2222-22-2-200-22002i−2i2i−2i−2i2i−2i2i0000000000000022-2-20000000000002i−2i000000
χ502-2-22-2-222-2222-22-2-200-22002i−2i2i−2i−2i2i−2i2i00000000000000-2-222000000000000−2i2i000000
χ512-2-22-2-222-2222-22-2-200-2200−2i2i−2i2i2i−2i2i−2i0000000000000022-2-2000000000000−2i2i000000
χ522-2-22-2-222-2222-22-2-200-2200−2i2i−2i2i2i−2i2i−2i00000000000000-2-2220000000000002i−2i000000
χ53444-4-4-4-44004-4400-4000000000000000000000000000022−2222−2200000000000000000000
χ54444-4-4-4-44004-4400-40000000000000000000000000000−2222−222200000000000000000000
χ55444-4-4-4-4400-44-4004000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ56444-4-4-4-4400-44-400400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ574-44-4-444-444000-4-4000000022−22−222222−22−222200000000000000000000000000000000000000
χ584-44-4-444-444000-4-40000000−222222−22−222222−2200000000000000000000000000000000000000
χ594-44-4-444-4-4-400044000000022−22−2222−222222−2200000000000000000000000000000000000000
χ604-44-4-444-4-4-4000440000000−222222−2222−22−222200000000000000000000000000000000000000
χ614-4-44-4-4444-4-4-44-44400-44000000000000000000000000000000000000000000000000
χ624-4-44-4-444-44-4-444-44004-4000000000000000000000000000000000000000000000000
χ634-4-4-444-44004-4-4004000000000000000000000000000022−22−222200000000000000000000
χ644-4-4-444-44004-4-40040000000000000000000000000000−222222−2200000000000000000000
χ654-4-4-444-4400-44400-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ664-4-4-444-4400-44400-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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