Finite Group Databasebeta

← Group #316728

Character table — Group #316728

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888244444888888888844444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111-1-1-1-111-1111111-111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-11111-1-1-1-1-1-1-11111-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-111-11111-1-11111-1-1
χ91111111111111111-1-1-1-1111111-11111-111-1-11111-1-1-111-1-111-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1111111-11111-111-1-11111-1-1-1-1-111-1-1-11111-1-1-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1111-1-111-1-111-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1111-1-1111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-11111-1-1-111-1-1-1-111-111-1-1-1-1-111-1-1-1-1111111
χ141111111111111111-1-1-1-111-1-1-1-1-11111-1-1-111-1-1-1-111-1-1-11111-1-1-1111111-1-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-11111111-1-1-1-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-11111
χ17222222222-222-2-22-222-2-2-2-20000222-2-2-200000000002000000-2000000000000
χ18222222222-222-2-22-222-2-2-2-200002-2-222-20000000000-20000002000000000000
χ19222222222-222-2-22-2-2-222-2-20000-222-2-220000000000-20000002000000000000
χ20222222222-222-2-22-2-2-222-2-20000-2-2-222200000000002000000-2000000000000
χ2122222222-22-2-222-2222-2-2-2-22222-200002-2-2-2-200002200000000000000000000
χ2222222222-22-2-222-2222-2-2-2-2-2-2-2-2-20000222220000-2-200000000000000000000
χ2322222222-22-2-222-22-2-222-2-2222220000-2-2-2220000-2-200000000000000000000
χ2422222222-22-2-222-22-2-222-2-2-2-2-2-220000-222-2-200002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222220000-20000-200002i2i−2i−2i00000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222220000-20000-20000−2i−2i2i2i0000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000020000200002i2i−2i−2i0000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002000020000−2i−2i2i2i00000000000000002i−2i0000
χ292-2-222-2-2222-2-22-22-200002-22i2i−2i−2i0000002i−2i0000000002i−2i002-20000000000000
χ302-2-222-2-2222-2-22-22-200002-22i2i−2i−2i0000002i−2i000000000−2i2i00-220000000000000
χ312-2-222-2-2222-2-22-22-200002-2−2i−2i2i2i000000−2i2i0000000002i−2i00-220000000000000
χ322-2-222-2-2222-2-22-22-200002-2−2i−2i2i2i000000−2i2i000000000−2i2i002-20000000000000
χ332-2-222-2-22-22222-2-2-20000-222i2i−2i−2i000000−2i2i000000000002i−2i0002-20000000000
χ342-2-222-2-22-22222-2-2-20000-222i2i−2i−2i000000−2i2i00000000000−2i2i000-220000000000
χ352-2-222-2-22-22222-2-2-20000-22−2i−2i2i2i0000002i−2i000000000002i−2i000-220000000000
χ362-2-222-2-22-22222-2-2-20000-22−2i−2i2i2i0000002i−2i00000000000−2i2i0002-20000000000
χ37444-44-4-4-40400-4-40400000000000000000000000000000000000022−2200000000
χ38444-44-4-4-40400-4-404000000000000000000000000000000000000−222200000000
χ39444-44-4-4-40-400440-400000000000000000000000000000000000000000022−2200
χ40444-44-4-4-40-400440-4000000000000000000000000000000000000000000−222200
χ4144-44-44-4-4404-400-400000000000000000000022−2222−220000000000000000000000
χ4244-44-44-4-4404-400-4000000000000000000000−2222−22220000000000000000000000
χ4344-44-44-4-4-40-440040000000000000000000002i2−2i2−2i22i20000000000000000000000
χ4444-44-44-4-4-40-44004000000000000000000000−2i22i22i2−2i20000000000000000000000
χ4544-4-4-4-444000000004i−4i000022−2222−22000000000000002i2−2i200000000000000000000
χ4644-4-4-4-444000000004i−4i0000−2222−222200000000000000−2i22i200000000000000000000
χ4744-4-4-4-44400000000−4i4i000022−2222−2200000000000000−2i22i200000000000000000000
χ4844-4-4-4-44400000000−4i4i0000−2222−2222000000000000002i2−2i200000000000000000000
χ494-444-4-44-440-4400-40000000000004-4000000000000000000000000000000000
χ504-444-4-44-440-4400-4000000000000-44000000000000000000000000000000000
χ514-444-4-44-4-404-4004000000000000004i−4i0000000000000000000000000000000
χ524-444-4-44-4-404-400400000000000000−4i4i0000000000000000000000000000000
χ534-44-4-44-4400000000004i−4i002i2−2i2−2i22i20000000022−2200000000000000000000000000
χ544-44-4-44-4400000000004i−4i00−2i22i22i2−2i200000000−222200000000000000000000000000
χ554-44-4-44-440000000000−4i4i002i2−2i2−2i22i200000000−222200000000000000000000000000
χ564-44-4-44-440000000000−4i4i00−2i22i22i2−2i20000000022−2200000000000000000000000000
χ574-4-444-4-444-4-4-4-44440000-440000000000000000000000000000000000000000
χ584-4-444-4-44-4-444-44-4400004-40000000000000000000000000000000000000000
χ594-4-4-4444-40400-440-4000000000000000000000000000000000000000000002i2−2i2
χ604-4-4-4444-40400-440-400000000000000000000000000000000000000000000−2i22i2
χ614-4-4-4444-40-4004-4040000000000000000000000000000000000000022−22000000
χ624-4-4-4444-40-4004-40400000000000000000000000000000000000000−2222000000

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