Finite Group Databasebeta

← Group #271332

Character table — Group #271332

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888888888888824444444888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111-1-1111-1-111111111-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-111
χ41111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-11-1-11111-1-1
χ51111111111111111111111-1-1111-1-111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1111111
χ71111111111111111111111-1-11-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ81111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111-1-1-1-111
χ91111111111111111-1-1-1-11111-111-1-1-1111111-1-1-1-11111-1-1-1-1-11-111-1-1-111-1-11-1
χ101111111111111111-1-1-1-11111-111-1-1-111-1-1-1-11111-1-1-1-11111-11-111-1-1-1-1-111-11
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-111-1-1111-1
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-11111-1-1-11
χ131111111111111111-1-1-1-111-1-1-11111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-11
χ141111111111111111-1-1-1-111-1-1-11111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-111111-11111-1-111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-11-11111-1-1-1-1111-1
χ172222222222-2-2-222-222-2-2-2-20022200-2-2-20000000000000000-20200000000000
χ182222222222-2-2-222-222-2-2-2-2002-2-200-222000000000000000020-200000000000
χ192222222222-2-2-222-2-2-222-2-200-222002-2-2000000000000000020-200000000000
χ202222222222-2-2-222-2-2-222-2-200-2-2-2002220000000000000000-20200000000000
χ2122222222-2-2222-2-222222-2-222-200-2-2-20000000000000000000-2000200000000
χ2222222222-2-2222-2-222222-2-2-2-2-20022-200000000000000000002000-200000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2222002220000000000000000000-2000-200000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2-2-2200-2-2200000000000000000002000200000000
χ2522222222-2-2-2-2-2-2-2-222-2-22200-2000020000000000000000000002-202-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200-200002000000000000000000000-220-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220020000-20000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220020000-2000000000000000000000-2202-2000000
χ292-2-2-222-222-222-22-2-200002-20002-20002-22i2i−2i−2i00002i2i−2i−2i000000000000000000
χ302-2-2-222-222-222-22-2-200002-20002-20002-2−2i−2i2i2i0000−2i−2i2i2i000000000000000000
χ312-2-2-222-222-222-22-2-200002-2000-22000-222i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ322-2-2-222-222-222-22-2-200002-2000-22000-22−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ332-2-2-222-222-2-2-222-220000-220002-2000-22000022-2-2000022-2-200000000000000
χ342-2-2-222-222-2-2-222-220000-220002-2000-220000-2-2220000-2-22200000000000000
χ352-2-2-222-222-2-2-222-220000-22000-220002-2000022-2-20000-2-22200000000000000
χ362-2-2-222-222-2-2-222-220000-22000-220002-20000-2-222000022-2-200000000000000
χ37444-4-44-4-4004-4400-400000000000000000000000000000000000000000022−2200
χ38444-4-44-4-4004-4400-4000000000000000000000000000000000000000000−222200
χ39444-4-44-4-400-44-400400000000000000000000000000000000000000002i2−2i20000
χ40444-4-44-4-400-44-40040000000000000000000000000000000000000000−2i22i20000
χ4144-44-4-4-4400000000004i−4i000000000000000000002i−2i2i−2i2-22-200000000000000
χ4244-44-4-4-4400000000004i−4i00000000000000000000−2i2i−2i2i-22-2200000000000000
χ4344-44-4-4-440000000000−4i4i000000000000000000002i−2i2i−2i-22-2200000000000000
χ4444-44-4-4-440000000000−4i4i00000000000000000000−2i2i−2i2i2-22-200000000000000
χ4544-4-44-44-44-4000-44000000000000000002i2−2i22i2−2i200000000000000000000000000
χ4644-4-44-44-44-4000-4400000000000000000−2i22i2−2i22i200000000000000000000000000
χ4744-4-44-44-4-440004-40000000000000000000002i2−2i22i2−2i20000000000000000000000
χ4844-4-44-44-4-440004-4000000000000000000000−2i22i2−2i22i20000000000000000000000
χ494-4444-4-4-444000-4-40000000000000000022−22−222200000000000000000000000000
χ504-4444-4-4-444000-4-400000000000000000−222222−2200000000000000000000000000
χ514-4444-4-4-4-4-4000440000000000000000000002i2−2i2−2i22i20000000000000000000000
χ524-4444-4-4-4-4-400044000000000000000000000−2i22i22i2−2i20000000000000000000000
χ534-44-4-4-444000000004-400000000000000000000002-2-222-2-2200000000000000
χ544-44-4-4-444000000004-40000000000000000000000-222-2-222-200000000000000
χ554-44-4-4-44400000000-4400000000000000000000002-2-22-222-200000000000000
χ564-44-4-4-44400000000-440000000000000000000000-222-22-2-2200000000000000
χ574-4-44-444-4004-4-4004000000000004-4000000000000000000000000000000000
χ584-4-44-444-4004-4-400400000000000-44000000000000000000000000000000000
χ594-4-44-444-400-44400-40000004i−4i00000000000000000000000000000000000000
χ604-4-44-444-400-44400-4000000−4i4i00000000000000000000000000000000000000
χ614-4-4-444-44-4444-4-44-40000-440000000000000000000000000000000000000000
χ624-4-4-444-44-44-4-44-44400004-40000000000000000000000000000000000000000

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