Finite Group Databasebeta

← Group #318373

Character table — Group #318373

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888822444444448888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ101111111111111111-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ111111111111111111-1-1-1-11111111111-1-1-1-1-111-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ121111111111111111-1-1-1-11111111111-1-1-1-1-111-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-111-1-111-1-1-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ172222222222-2-2-222-22222-2-20000000022-2-2-222-2-2-20000000000000000000000000000
χ182222222222-2-2-222-22222-2-200000000-2-2-222-2-2-2220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000222-2-2-2-22220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-200000000-2-2222222-2-20000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-22222-2-2-2-20020000-20022-2-2000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-2-222220020000-200-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-222-2-22222-2-2-2-200-20000200-2-222000000000000000000000000
χ2422222222-2-2222-2-22-2-222-2-2-2-2-2-2222200-2000020022-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220000000000-2000020000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000000000-200002000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000000020000-20000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222000000000020000-2000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-22-22-2-22-20002-202-22-200i2i2−i2−i2i2i2−i2−i20002i−2i0002i−2ii2−i2i2−i22−22−22−22−20000000000000000
χ3022-22-22-2-22-20002-202-22-200i2i2−i2−i2i2i2−i2−i2000−2i2i000−2i2ii2−i2i2−i2−22−22−22−220000000000000000
χ3122-22-22-2-22-20002-202-22-200−i2−i2i2i2−i2−i2i2i20002i−2i0002i−2i−i2i2−i2i2−22−22−22−220000000000000000
χ3222-22-22-2-22-20002-202-22-200−i2−i2i2i2−i2−i2i2i2000−2i2i000−2i2i−i2i2−i2i22−22−22−22−20000000000000000
χ3322-22-22-2-22-20002-20-22-2200i2i2−i2−i2i2i2−i2−i20002i−2i000−2i2i−i2i2−i2i22−22−2−22−220000000000000000
χ3422-22-22-2-22-20002-20-22-2200i2i2−i2−i2i2i2−i2−i2000−2i2i0002i−2i−i2i2−i2i2−22−222−22−20000000000000000
χ3522-22-22-2-22-20002-20-22-2200−i2−i2i2i2−i2−i2i2i20002i−2i000−2i2ii2−i2i2−i2−22−222−22−20000000000000000
χ3622-22-22-2-22-20002-20-22-2200−i2−i2i2i2−i2−i2i2i2000−2i2i0002i−2ii2−i2i2−i22−22−2−22−220000000000000000
χ3722-22-22-2-2-22000-2202-2-2200i2i2−i2−i2−i2−i2i2i22-20002-2000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ3822-22-22-2-2-22000-2202-2-2200i2i2−i2−i2−i2−i2i2i2-22000-22000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ3922-22-22-2-2-22000-2202-2-2200−i2−i2i2i2i2i2−i2−i22-20002-2000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ4022-22-22-2-2-22000-2202-2-2200−i2−i2i2i2i2i2−i2−i2-22000-22000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ4122-22-22-2-2-22000-220-222-200i2i2−i2−i2−i2−i2i2i22-2000-22000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ4222-22-22-2-2-22000-220-222-200i2i2−i2−i2−i2−i2i2i2-220002-2000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ4322-22-22-2-2-22000-220-222-200−i2−i2i2i2i2i2−i2−i22-2000-22000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ4422-22-22-2-2-22000-220-222-200−i2−i2i2i2i2i2−i2−i2-220002-2000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ452-2-222-2-22222-2-2-2-2200002-22-22-22-22-20000000000000000000000002i−2i2i−2i0000000000
χ462-2-222-2-22222-2-2-2-2200002-22-22-22-22-2000000000000000000000000−2i2i−2i2i0000000000
χ472-2-222-2-22222-2-2-2-2200002-2-22-22-22-220000000000000000000000002i−2i−2i2i0000000000
χ482-2-222-2-22222-2-2-2-2200002-2-22-22-22-22000000000000000000000000−2i2i2i−2i0000000000
χ492-2-222-2-22-2-22-2-22220000-222-22-2-22-2200000000000000000000002-200002-200000000
χ502-2-222-2-22-2-22-2-22220000-222-22-2-22-220000000000000000000000-220000-2200000000
χ512-2-222-2-22-2-22-2-22220000-22-22-222-22-200000000000000000000002-20000-2200000000
χ522-2-222-2-22-2-22-2-22220000-22-22-222-22-20000000000000000000000-2200002-200000000
χ53444-44-4-4-40044-400-40000000000000000000000000000000000000000000022−22000000
χ54444-44-4-4-40044-400-400000000000000000000000000000000000000000000−2222000000
χ55444-44-4-4-400-4-4400400000000000000000000000000000000000000000000002i2−2i20000
χ56444-44-4-4-400-4-440040000000000000000000000000000000000000000000000−2i22i20000
χ574-444-4-44-44-4000-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ584-444-4-44-44-4000-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-444-4-44-4-440004-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ604-444-4-44-4-440004-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-444-4-4444-444-4-4-40000-440000000000000000000000000000000000000000000000
χ624-4-444-4-44-4-4-44444-400004-40000000000000000000000000000000000000000000000
χ634-4-4-4444-4004-4400-40000000000000000000000000000000000000000000000002i2−2i200
χ644-4-4-4444-4004-4400-4000000000000000000000000000000000000000000000000−2i22i200
χ654-4-4-4444-400-44-40040000000000000000000000000000000000000000000000000022−22
χ664-4-4-4444-400-44-400400000000000000000000000000000000000000000000000000−2222
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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