Finite Group Databasebeta

← Group #316869

Character table — Group #316869

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
χ1722222222222-2-2-2-2222-2-2-2-22222-2-2-2-2002000000-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2-2-22222002000000-2-2-222000000000000000000000000
χ1922222222222-2-2-2-22-2-222-2-22222-2-2-2-200-20000002-2-222000000000000000000000000
χ2022222222222-2-2-2-22-2-222-2-2-2-2-2-2222200-2000000222-2-2000000000000000000000000
χ2122222222-2-2-22222-22222-2-20000000022-2-2-2-2-222-20000000000000000000000000000
χ2222222222-2-2-22222-22222-2-200000000-2-2-22222-2-2-20000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-20000000022222-2-2-2-220000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-200000000-2-22-2-2222220000000000000000000000000000
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
χ2922-2-22-2-2200022-2-202i−2i2i−2i00i2i2−i2−i2i2i2−i2−i20002-22i−2i0002−22−22−22−2i2−i2i2−i20000000000000000
χ3022-2-22-2-2200022-2-202i−2i2i−2i00i2i2−i2−i2i2i2−i2−i2000-22−2i2i0002−22−2−22−22−i2i2−i2i20000000000000000
χ3122-2-22-2-2200022-2-202i−2i2i−2i00−i2−i2i2i2−i2−i2i2i20002-22i−2i000−22−22−22−22−i2i2−i2i20000000000000000
χ3222-2-22-2-2200022-2-202i−2i2i−2i00−i2−i2i2i2−i2−i2i2i2000-22−2i2i000−22−222−22−2i2−i2i2−i20000000000000000
χ3322-2-22-2-2200022-2-20−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i20002-2−2i2i000−22−22−22−22i2−i2i2−i20000000000000000
χ3422-2-22-2-2200022-2-20−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i2000-222i−2i000−22−222−22−2−i2i2−i2i20000000000000000
χ3522-2-22-2-2200022-2-20−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i20002-2−2i2i0002−22−22−22−2−i2i2−i2i20000000000000000
χ3622-2-22-2-2200022-2-20−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i2000-222i−2i0002−22−2−22−22i2−i2i2−i20000000000000000
χ3722-2-22-2-22000-2-22202i−2i−2i2i00i2i2−i2−i2−i2−i2i2i22-2000002i−2i02−2−22i2−i2−i2i2−222−20000000000000000
χ3822-2-22-2-22000-2-22202i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2-2200000−2i2i02−2−22−i2i2i2−i22−2−220000000000000000
χ3922-2-22-2-22000-2-22202i−2i−2i2i00−i2−i2i2i2i2i2−i2−i22-2000002i−2i0−222−2−i2i2i2−i22−2−220000000000000000
χ4022-2-22-2-22000-2-22202i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2-2200000−2i2i0−222−2i2−i2−i2i2−222−20000000000000000
χ4122-2-22-2-22000-2-2220−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i22-200000−2i2i0−222−2i2−i2−i2i22−2−220000000000000000
χ4222-2-22-2-22000-2-2220−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2-22000002i−2i0−222−2−i2i2i2−i2−222−20000000000000000
χ4322-2-22-2-22000-2-2220−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i22-200000−2i2i02−2−22−i2i2i2−i2−222−20000000000000000
χ4422-2-22-2-22000-2-2220−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2-22000002i−2i02−2−22i2−i2−i2i22−2−220000000000000000
χ452-2-2-2222-222-22-22-2-200002-22i−2i2i−2i2i−2i2i−2i0000000000000000000000002-22i−2i0000000000
χ462-2-2-2222-222-22-22-2-200002-22i−2i2i−2i2i−2i2i−2i000000000000000000000000-22−2i2i0000000000
χ472-2-2-2222-222-22-22-2-200002-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000002-2−2i2i0000000000
χ482-2-2-2222-222-22-22-2-200002-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000-222i−2i0000000000
χ492-2-2-2222-222-2-22-22-20000-222i−2i2i−2i−2i2i−2i2i00000000000000000000002-200002i−2i00000000
χ502-2-2-2222-222-2-22-22-20000-222i−2i2i−2i−2i2i−2i2i0000000000000000000000-220000−2i2i00000000
χ512-2-2-2222-222-2-22-22-20000-22−2i2i−2i2i2i−2i2i−2i00000000000000000000002-20000−2i2i00000000
χ522-2-2-2222-222-2-22-22-20000-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000-2200002i−2i00000000
χ53444-4-44-4-44-440000-40000000000000000000000000000000000000000000022−22000000
χ54444-4-44-4-44-440000-400000000000000000000000000000000000000000000−2222000000
χ55444-4-44-4-4-44-40000400000000000000000000000000000000000000000000002i2−2i20000
χ56444-4-44-4-4-44-4000040000000000000000000000000000000000000000000000−2i22i20000
χ574-4444-4-4-40004-4-44000000022−22−222222−22−222200000000000000000000000000000000000000
χ584-4444-4-4-40004-4-440000000−222222−22−222222−2200000000000000000000000000000000000000
χ594-4444-4-4-4000-444-4000000022−22−2222−222222−2200000000000000000000000000000000000000
χ604-4444-4-4-4000-444-40000000−222222−2222−22−222200000000000000000000000000000000000000
χ614-4-44-44-444-4-40000400000000000000000000000000000000000000000000000022−2200
χ624-4-44-44-444-4-400004000000000000000000000000000000000000000000000000−222200
χ634-4-44-44-44-4440000-4000000000000000000000000000000000000000000000000002i2−2i2
χ644-4-44-44-44-4440000-400000000000000000000000000000000000000000000000000−2i22i2
χ654-4-4-4444-4-4-444-44-440000-440000000000000000000000000000000000000000000000
χ664-4-4-4444-4-4-44-44-44400004-40000000000000000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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