Finite Group Databasebeta

← Group #281739

Character table — Group #281739

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444488888888888888882244444448888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ91111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ101111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1111111-1-1-1-1-1-111111-1
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-1111111-1-1-1-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-111-1-111-1-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-111-1-111-1-1111-1
χ172222222222-2-2-22-2222-2-2-2-222000000000000000022-2-2-2-2-2220000000000000000000000
χ182222222222-2-2-22-2222-2-2-2-2220000000000000000-2-2-22222-2-20000000000000000000000
χ192222222222-2-2-22-22-2-2-2-222-2-2000000000000000022222-2-2-2-20000000000000000000000
χ202222222222-2-2-22-22-2-2-2-222-2-20000000000000000-2-22-2-222220000000000000000000000
χ2122222222-2-2222-22-222-2-222-2-2222222220000000000-2000000-2-2-2-2000000000000000000
χ2222222222-2-2222-22-222-2-222-2-2-2-2-2-2-2-2-2-20000000000-20000002222000000000000000000
χ2322222222-2-2222-22-2-2-2-2-2-2-2222222-2-2-2-200000000002000000-2-222000000000000000000
χ2422222222-2-2222-22-2-2-2-2-2-2-222-2-2-2-222220000000000200000022-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i00200000000002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i0020000000000−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i00-20000000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i00-200000000002i2i−2i−2i00000000000000
χ2922-2-2-2-22222000-20-22-200002-222−2−222−2−2i2i2−i2−i2i2i2−i2−i20002i−2i2i−2i002−22−2i2−i2i2−i200000000000000
χ3022-2-2-2-22222000-20-22-200002-222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000−2i2i−2i2i002−22−2−i2i2−i2i200000000000000
χ3122-2-2-2-22222000-20-22-200002-2−2−222−2−222i2i2−i2−i2i2i2−i2−i2000−2i2i−2i2i00−22−22i2−i2i2−i200000000000000
χ3222-2-2-2-22222000-20-22-200002-2−2−222−2−222−i2−i2i2i2−i2−i2i2i20002i−2i2i−2i00−22−22−i2i2−i2i200000000000000
χ3322-2-2-2-22222000-20-2-220000-2222−2−2−2−222i2i2−i2−i2i2i2−i2−i20002i−2i−2i2i002−2−22−i2i2−i2i200000000000000
χ3422-2-2-2-22222000-20-2-220000-2222−2−2−2−222−i2−i2i2i2−i2−i2i2i2000−2i2i2i−2i002−2−22i2−i2i2−i200000000000000
χ3522-2-2-2-22222000-20-2-220000-22−2−22222−2−2i2i2−i2−i2i2i2−i2−i2000−2i2i2i−2i00−222−2−i2i2−i2i200000000000000
χ3622-2-2-2-22222000-20-2-220000-22−2−22222−2−2−i2−i2i2i2−i2−i2i2i20002i−2i−2i2i00−222−2i2−i2i2−i200000000000000
χ3722-2-2-2-222-2-20002022-20000-2222−2−222−2−222−2−2−2−2222-2000002-2−22−222−2−2200000000000000
χ3822-2-2-2-222-2-20002022-20000-2222−2−222−2−2−2−22222−2−2-2200000-22−22−22−222−200000000000000
χ3922-2-2-2-222-2-20002022-20000-22−2−222−2−22222−2−2−2−222-2200000-222−22−22−2−2200000000000000
χ4022-2-2-2-222-2-20002022-20000-22−2−222−2−222−2−22222−2−22-2000002-22−22−2−222−200000000000000
χ4122-2-2-2-222-2-2000202-2200002-222−2−2−2−22222−2−2−2−222-22000002-2−222−2−222−200000000000000
χ4222-2-2-2-222-2-2000202-2200002-222−2−2−2−222−2−22222−2−22-200000-22−222−22−2−2200000000000000
χ4322-2-2-2-222-2-2000202-2200002-2−2−22222−2−222−2−2−2−2222-200000-222−2−22−222−200000000000000
χ4422-2-2-2-222-2-2000202-2200002-2−2−22222−2−2−2−22222−2−2-22000002-22−2−222−2−2200000000000000
χ452-2-22-22-222-222-22-2-2002-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000002-200002i−2i0000
χ462-2-22-22-222-222-22-2-2002-20000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000-220000−2i2i0000
χ472-2-22-22-222-222-22-2-2002-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000002-20000−2i2i0000
χ482-2-22-22-222-222-22-2-2002-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000-2200002i−2i0000
χ492-2-22-22-22-22-2-22-222002-20000000000002-22-2-22-22000000000000000002-200002-2000000
χ502-2-22-22-22-22-2-22-222002-20000000000002-22-2-22-2200000000000000000-220000-22000000
χ512-2-22-22-22-22-2-22-222002-2000000000000-22-222-22-2000000000000000002-20000-22000000
χ522-2-22-22-22-22-2-22-222002-2000000000000-22-222-22-200000000000000000-2200002-2000000
χ53444-4-44-4-4004-440-4000000000000000000000000000000000000000000000000000022−2200
χ54444-4-44-4-4004-440-40000000000000000000000000000000000000000000000000000−222200
χ55444-4-44-4-400-44-40400000000000000000000000000000000000000000000002i2−2i200000000
χ56444-4-44-4-400-44-4040000000000000000000000000000000000000000000000−2i22i200000000
χ574-444-4-44-40000000000004i−4i0022−2222−222i2−2i22i2−2i2000000000000000000000000000000000000000
χ584-444-4-44-40000000000004i−4i00−2222−2222−2i22i2−2i22i2000000000000000000000000000000000000000
χ594-444-4-44-4000000000000−4i4i0022−2222−22−2i22i2−2i22i2000000000000000000000000000000000000000
χ604-444-4-44-4000000000000−4i4i00−2222−22222i2−2i22i2−2i2000000000000000000000000000000000000000
χ614-44-44-4-444-4000-404000000000000000022−22−222222−22−22220000000000000000000000000000000
χ624-44-44-4-444-4000-4040000000000000000−222222−22−222222−220000000000000000000000000000000
χ634-44-44-4-44-4400040-400000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ644-44-44-4-44-4400040-40000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ654-4-44-44-444-4-4-4444-400-44000000000000000000000000000000000000000000000000000
χ664-4-44-44-44-4444-4-4-4400-44000000000000000000000000000000000000000000000000000
χ674-4-4-4444-4004-4-4040000000004-4-440000000000000000000000000000000000000000000
χ684-4-4-4444-4004-4-404000000000-444-40000000000000000000000000000000000000000000
χ694-4-4-4444-400-4440-400000000000004i−4i−4i4i000000000000000000000000000000000000000
χ704-4-4-4444-400-4440-40000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ7188-888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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