Finite Group Databasebeta

← Group #288278

Character table — Group #288278

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882224444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-111-11-1111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-11-11-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-11111-1-11-1
χ91111111111111111-1-1-1-111111111-1-11111-1-1-1-111111111-1-1-11-11-1-1-1-11111-1-1
χ101111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-11-111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-11-1-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-111-1-1-1-1-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-11-1-11111-1-1111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111-111-1-111-1-1-11
χ172222222222-22-2-2-222222-2-2000000-2-20022000000-2-200000020-200000000000
χ182222222222-22-2-2-222222-2-2000000-2-200-2-200000022000000-20200000000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000000220022000000-2-2000000-20200000000000
χ202222222222-22-2-2-22-2-2-2-2-2-20000002200-2-20000002200000020-200000000000
χ2122222222-2-22-2222-20000-2-22222220022000000-2-2000000000-20-20000000000
χ2222222222-2-22-2222-20000-2-22222-2-200-2-2000000-2-20000000002020000000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-22200-2-20000002200000000020-20000000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-2-2-2002200000022000000000-2020000000000
χ2522-2-22-2-22222-2-22-2-22i2i−2i−2i-220000002i−2i00000000000022-2-2000000002i−2i000000
χ2622-2-22-2-22222-2-22-2-22i2i−2i−2i-220000002i−2i000000000000-2-22200000000−2i2i000000
χ2722-2-22-2-22222-2-22-2-2−2i−2i2i2i-22000000−2i2i00000000000022-2-200000000−2i2i000000
χ2822-2-22-2-22222-2-22-2-2−2i−2i2i2i-22000000−2i2i000000000000-2-222000000002i−2i000000
χ2922-2-22-2-2222-2-22-22-22i2i−2i−2i2-222-2-200−2i2i00002i2i−2i−2i2-20000000000000000000000
χ3022-2-22-2-2222-2-22-22-22i2i−2i−2i2-2-2-22200−2i2i0000−2i−2i2i2i-220000000000000000000000
χ3122-2-22-2-2222-2-22-22-2−2i−2i2i2i2-222-2-2002i−2i0000−2i−2i2i2i2-20000000000000000000000
χ3222-2-22-2-2222-2-22-22-2−2i−2i2i2i2-2-2-222002i−2i00002i2i−2i−2i-220000000000000000000000
χ3322-2-22-2-22-2-2-222-2220000-2222-2-2000000000000-220000002-200002-200000000
χ3422-2-22-2-22-2-2-222-2220000-2222-2-2000000000000-22000000-220000-2200000000
χ3522-2-22-2-22-2-2-222-2220000-22-2-2220000000000002-20000002-20000-2200000000
χ3622-2-22-2-22-2-2-222-2220000-22-2-2220000000000002-2000000-2200002-200000000
χ3744444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ38444-4-44-4-44-404000-400000000000000000022−2222−22000000000000000000000000
χ39444-4-44-4-44-404000-4000000000000000000−2222−2222000000000000000000000000
χ40444-4-44-4-4-440-400044i−4i4i−4i000000000000000000000000000000000000000000
χ41444-4-44-4-4-440-40004−4i4i−4i4i000000000000000000000000000000000000000000
χ4244-44-4-44-44-40-400040000000000000000002i2−2i2−2i22i2000000000000000000000000
χ4344-44-4-44-44-40-40004000000000000000000−2i22i22i2−2i2000000000000000000000000
χ4444-44-4-44-4-4404000-44-4-44000000000000000000000000000000000000000000
χ4544-44-4-44-4-4404000-4-444-4000000000000000000000000000000000000000000
χ4644-4-44-4-44-4-444-44-4400004-40000000000000000000000000000000000000000
χ474-4444-4-4-400404-4-4000000000000000000000000000000000000000000022−2200
χ484-4444-4-4-400404-4-40000000000000000000000000000000000000000000−222200
χ494-4444-4-4-400-40-4440000000000000004i−4i000000000000000000000000000000
χ504-4444-4-4-400-40-444000000000000000−4i4i000000000000000000000000000000
χ514-44-4-4-4440000000000000022−2222−2200000022−22000000002-22-20000000000000000
χ524-44-4-4-4440000000000000022−2222−22000000−222200000000-22-220000000000000000
χ534-44-4-4-44400000000000000−2222−222200000022−2200000000-22-220000000000000000
χ544-44-4-4-44400000000000000−2222−2222000000−2222000000002-22-20000000000000000
χ554-4-44-44-440000000000000022−22−22220000000000000022−222-2-220000000000000000
χ564-4-44-44-440000000000000022−22−222200000000000000−2222-222-20000000000000000
χ574-4-44-44-4400000000000000−222222−220000000000000022−22-222-20000000000000000
χ584-4-44-44-4400000000000000−222222−2200000000000000−22222-2-220000000000000000
χ594-4-4-4444-40040-4-44000000000004i−4i0000000000000000000000000000000000
χ604-4-4-4444-40040-4-4400000000000−4i4i0000000000000000000000000000000000
χ614-4-4-4444-400-4044-4000000000000000000000000000000000000000002i2−2i20000
χ624-4-4-4444-400-4044-400000000000000000000000000000000000000000−2i22i20000

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