Finite Group Databasebeta

← Group #316839

Character table — Group #316839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888822444444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111111111-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ101111111111111111-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ111111111111111111-1-1-1-11111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ121111111111111111-1-1-1-11111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-111-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ172222222222-2-2-222-22222-2-20000000022-222-2-2-2-2-20000000000000000000000000000
χ182222222222-2-2-222-22222-2-200000000-2-2-2-2-22222-20000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000222-2-2-2-22220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-200000000-2-222222-2-220000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-22222-2-2-2-2002000000-222-2-2000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-2-22222002000000-2-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-222-2-22222-2-2-2-200-20000002-2-222000000000000000000000000
χ2422222222-2-2222-2-22-2-222-2-2-2-2-2-2222200-2000000222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220000000000-2000000200002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000000000-200000020000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200000000002000000-200002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000002000000-20000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-22-2-2-222000-2-202-22-20022−2−222−2−22-202-2000002−22−22−22−22−22−20000000000000000
χ30222-22-2-2-222000-2-202-22-20022−2−222−2−2-220-22000002−22−2−22−22−22−220000000000000000
χ31222-22-2-2-222000-2-202-22-200−2−222−2−2222-202-200000−22−22−22−22−22−220000000000000000
χ32222-22-2-2-222000-2-202-22-200−2−222−2−222-220-2200000−22−222−22−22−22−20000000000000000
χ33222-22-2-2-222000-2-20-22-220022−2−222−2−22-20-2200000−22−222−22−2−22−220000000000000000
χ34222-22-2-2-222000-2-20-22-220022−2−222−2−2-2202-200000−22−22−22−222−22−20000000000000000
χ35222-22-2-2-222000-2-20-22-2200−2−222−2−2222-20-22000002−22−2−22−222−22−20000000000000000
χ36222-22-2-2-222000-2-20-22-2200−2−222−2−222-2202-2000002−22−22−22−2−22−220000000000000000
χ37222-22-2-2-2-2-20002202-2-220022−2−2−2−222000002i−2i2i−2i02−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ38222-22-2-2-2-2-20002202-2-220022−2−2−2−22200000−2i2i−2i2i02−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ39222-22-2-2-2-2-20002202-2-2200−2−22222−2−2000002i−2i2i−2i0−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ40222-22-2-2-2-2-20002202-2-2200−2−22222−2−200000−2i2i−2i2i0−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ41222-22-2-2-2-2-2000220-222-20022−2−2−2−222000002i−2i−2i2i0−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ42222-22-2-2-2-2-2000220-222-20022−2−2−2−22200000−2i2i2i−2i0−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ43222-22-2-2-2-2-2000220-222-200−2−22222−2−2000002i−2i−2i2i02−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ44222-22-2-2-2-2-2000220-222-200−2−22222−2−200000−2i2i2i−2i02−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ452-2-2-2222-22-222-22-2-200002-22i−2i2i−2i2i−2i2i−2i0000000000000000000000002-22i−2i0000000000
χ462-2-2-2222-22-222-22-2-200002-22i−2i2i−2i2i−2i2i−2i000000000000000000000000-22−2i2i0000000000
χ472-2-2-2222-22-222-22-2-200002-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000002-2−2i2i0000000000
χ482-2-2-2222-22-222-22-2-200002-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000-222i−2i0000000000
χ492-2-2-2222-2-2222-2-22-20000-222i−2i2i−2i−2i2i−2i2i00000000000000000000002-200002i−2i00000000
χ502-2-2-2222-2-2222-2-22-20000-222i−2i2i−2i−2i2i−2i2i0000000000000000000000-220000−2i2i00000000
χ512-2-2-2222-2-2222-2-22-20000-22−2i2i−2i2i2i−2i2i−2i00000000000000000000002-20000−2i2i00000000
χ522-2-2-2222-2-2222-2-22-20000-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000-2200002i−2i00000000
χ5344-44-44-4-4004-4400-40000000000000000000000000000000000000000000022−22000000
χ5444-44-44-4-4004-4400-400000000000000000000000000000000000000000000−2222000000
χ5544-44-44-4-400-44-400400000000000000000000000000000000000000000000002i2−2i20000
χ5644-44-44-4-400-44-40040000000000000000000000000000000000000000000000−2i22i20000
χ574-44-4-44-44004-4-400400000000000000000000000000000000000000000000000022−2200
χ584-44-4-44-44004-4-4004000000000000000000000000000000000000000000000000−222200
χ594-44-4-44-4400-44400-4000000000000000000000000000000000000000000000000002i2−2i2
χ604-44-4-44-4400-44400-400000000000000000000000000000000000000000000000000−2i22i2
χ614-4-444-4-444-4000-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ624-4-444-4-444-4000-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ634-4-444-4-44-440004-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ644-4-444-4-44-440004-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ654-4-4-4444-44-4-4-444-440000-440000000000000000000000000000000000000000000000
χ664-4-4-4444-4-44-4-44-44400004-40000000000000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-888-8-88-8000000000000000000000000000000000000000000000000000000000000

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