Finite Group Databasebeta

← Group #318377

Character table — Group #318377

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888822444444448888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111111111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222-2-2-222-222-2-2220000000022-2-2-2-222-2-20000000000000000000000000000
χ182222222222-2-2-222-222-2-22200000000-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-2000000002222-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-200000000-2-2222222-2-20000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-22222-2-2-2-2002-200000022-2-2000000000000000000000000
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
χ2522222222-2-2-2-2-2-2-2-22222-2-20000000000-2200000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000000000-220000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200000000002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-2-22-22-20002-202i−2i002i−2i22−2−222−2−200002i−2i002-2i2−i2i2−i2i2−i2i2−i22−22−20000000000000000
χ30222-2-2-22-22-20002-202i−2i002i−2i22−2−222−2−20000−2i2i00-22i2−i2i2−i2−i2i2−i2i2−22−220000000000000000
χ31222-2-2-22-22-20002-202i−2i002i−2i−2−222−2−22200002i−2i002-2−i2i2−i2i2−i2i2−i2i2−22−220000000000000000
χ32222-2-2-22-22-20002-202i−2i002i−2i−2−222−2−2220000−2i2i00-22−i2i2−i2i2i2−i2i2−i22−22−20000000000000000
χ33222-2-2-22-22-20002-20−2i2i00−2i2i22−2−222−2−200002i−2i00-22−i2i2−i2i2i2−i2i2−i2−22−220000000000000000
χ34222-2-2-22-22-20002-20−2i2i00−2i2i22−2−222−2−20000−2i2i002-2−i2i2−i2i2−i2i2−i2i22−22−20000000000000000
χ35222-2-2-22-22-20002-20−2i2i00−2i2i−2−222−2−22200002i−2i00-22i2−i2i2−i2−i2i2−i2i22−22−20000000000000000
χ36222-2-2-22-22-20002-20−2i2i00−2i2i−2−222−2−2220000−2i2i002-2i2−i2i2−i2i2−i2i2−i2−22−220000000000000000
χ37222-2-2-22-2-22000-2202i−2i00−2i2i22−2−2−2−2222-200002i−2i00i2−i2−i2i22−2−22−i2i2i2−i20000000000000000
χ38222-2-2-22-2-22000-2202i−2i00−2i2i22−2−2−2−222-220000−2i2i00i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ39222-2-2-22-2-22000-2202i−2i00−2i2i−2−22222−2−22-200002i−2i00−i2i2i2−i2−222−2i2−i2−i2i20000000000000000
χ40222-2-2-22-2-22000-2202i−2i00−2i2i−2−22222−2−2-220000−2i2i00−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ41222-2-2-22-2-22000-220−2i2i002i−2i22−2−2−2−2222-20000−2i2i00−i2i2i2−i22−2−22i2−i2−i2i20000000000000000
χ42222-2-2-22-2-22000-220−2i2i002i−2i22−2−2−2−222-2200002i−2i00−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ43222-2-2-22-2-22000-220−2i2i002i−2i−2−22222−2−22-20000−2i2i00i2−i2−i2i2−222−2−i2i2i2−i20000000000000000
χ44222-2-2-22-2-22000-220−2i2i002i−2i−2−22222−2−2-2200002i−2i00i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ452-2-2-2222-2222-2-2-2-22002-2002-22-22-22-2000000000000000000000000002i−2i2i−2i00000000
χ462-2-2-2222-2222-2-2-2-22002-2002-22-22-22-200000000000000000000000000−2i2i−2i2i00000000
χ472-2-2-2222-2222-2-2-2-22002-200-22-22-22-22000000000000000000000000002i−2i−2i2i00000000
χ482-2-2-2222-2222-2-2-2-22002-200-22-22-22-2200000000000000000000000000−2i2i2i−2i00000000
χ492-2-2-2222-2-2-22-2-222200-22002-22-2-22-2200000000000000000000002-22-2000000000000
χ502-2-2-2222-2-2-22-2-222200-22002-22-2-22-220000000000000000000000-22-22000000000000
χ512-2-2-2222-2-2-22-2-222200-2200-22-222-22-200000000000000000000002-2-22000000000000
χ522-2-2-2222-2-2-22-2-222200-2200-22-222-22-20000000000000000000000-222-2000000000000
χ5344-444-4-4-40044-400-40000000000000000000000000000000000000000000022−22000000
χ5444-444-4-4-40044-400-400000000000000000000000000000000000000000000−2222000000
χ5544-444-4-4-400-4-4400400000000000000000000000000000000000000000000002i2−2i20000
χ5644-444-4-4-400-4-440040000000000000000000000000000000000000000000000−2i22i20000
χ574-44-44-4-44004-4400-40000000000000000000000000000000000000000000000002i2−2i200
χ584-44-44-4-44004-4400-4000000000000000000000000000000000000000000000000−2i22i200
χ594-44-44-4-4400-44-40040000000000000000000000000000000000000000000000000022−22
χ604-44-44-4-4400-44-400400000000000000000000000000000000000000000000000000−2222
χ614-4-44-4-4444-4000-44000000022−22−222222−22−222200000000000000000000000000000000000000
χ624-4-44-4-4444-4000-440000000−222222−22−222222−2200000000000000000000000000000000000000
χ634-4-44-4-444-440004-4000000022−22−2222−222222−2200000000000000000000000000000000000000
χ644-4-44-4-444-440004-40000000−222222−2222−22−222200000000000000000000000000000000000000
χ654-4-4-4444-444-444-4-4-400-44000000000000000000000000000000000000000000000000
χ664-4-4-4444-4-4-4-44444-4004-4000000000000000000000000000000000000000000000000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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