Finite Group Databasebeta

← Group #251613

Character table — Group #251613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444442224444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-11-1-1-11-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111
χ511111111111111111111111-1-1-1-111111-1-1-1-111111111-111-1-111-111-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111
χ711111111111111111111111-1-1-1-11-1-1-1-11111111111111-1-1-11-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1111-1111111-1-1-1-1
χ91111111111111111-1-11-1-11-111-1-1-1111111-1-11111-1-1-1-11-1-1-1-1111-1-111-1-111-1-1
χ101111111111111111-1-11-1-11-111-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1111-1-111-1-111
χ111111111111111111-1-11-1-11-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-11-1-111111-1-1-1-111
χ121111111111111111-1-11-1-11-111-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-11111-1-1-1-11111-1-1
χ131111111111111111-1-11-1-11-1-1-111-11111-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-111-1-111
χ141111111111111111-1-11-1-11-1-1-111-11111-1-111-1-1-1-11111-1-1-111-1-1-11111-1-111-1-1
χ151111111111111111-1-11-1-11-1-1-111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-11-1-11-1-1-111-1-1-1-1-111-1-1-1-1-1-111111111-111-1-1-111-1-1-1-111
χ172222222222-2-222-2-222-2-2-2-2222-2-2-200000000000000000002000-20000000000
χ182222222222-2-222-2-222-2-2-2-22-2-222-20000000000000000000-200020000000000
χ192222222222-2-222-2-2-2-2-222-2-2222220000000000000000000-2000-20000000000
χ202222222222-2-222-2-2-2-2-222-2-2-2-2-2-220000000000000000000200020000000000
χ2122222222-2-222-2-22222-2-2-2-2-200002000022-2-200000000-200020000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2000020000-2-222000000002000-20000000000000
χ2322222222-2-222-2-222-2-2-222-220000-20000222200000000-2000-20000000000000
χ2422222222-2-222-2-222-2-2-222-220000-20000-2-2-2-200000000200020000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-20000-222-2-200000000000002-2000000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-20000-2-2-2220000000000000-22000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22-2-2220000222-2-20000000000000-22000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22-2-22200002-2-22200000000000002-2000000000000000
χ292-22-2-22-222-22-22-22-200200-20000002i−2i2i−2i000000002i2i−2i−2i000000002-200000000
χ302-22-2-22-222-22-22-22-200200-20000002i−2i2i−2i00000000−2i−2i2i2i00000000-2200000000
χ312-22-2-22-222-22-22-22-200200-2000000−2i2i−2i2i000000002i2i−2i−2i00000000-2200000000
χ322-22-2-22-222-22-22-22-200200-2000000−2i2i−2i2i00000000−2i−2i2i2i000000002-200000000
χ332-22-2-22-22-22-22-22-2200200-20000002i−2i−2i2i00002i2i−2i−2i0000000002-200000000000
χ342-22-2-22-22-22-22-22-2200200-20000002i−2i−2i2i0000−2i−2i2i2i000000000-2200000000000
χ352-22-2-22-22-22-22-22-2200200-2000000−2i2i2i−2i00002i2i−2i−2i000000000-2200000000000
χ362-22-2-22-22-22-22-22-2200200-2000000−2i2i2i−2i0000−2i−2i2i2i0000000002-200000000000
χ37444-44-4-4-44-400-4400000000000000000000000000000000000000000022−220000
χ38444-44-4-4-44-400-44000000000000000000000000000000000000000000−22220000
χ39444-44-4-4-4-44004-4000000000000000000000000000000000000000022−22000000
χ40444-44-4-4-4-44004-40000000000000000000000000000000000000000−2222000000
χ4144-44-4-4-44004400-4-40000000000000000000000000000000000000000000022−22
χ4244-44-4-4-44004400-4-400000000000000000000000000000000000000000000−2222
χ4344-44-4-4-4400-4-400440000000000000000000000000000000000000000002i2−2i200
χ4444-44-4-4-4400-4-40044000000000000000000000000000000000000000000−2i22i200
χ4544-4-4-444-4000000000004i−4i0000000000000002-22-22i−2i2i−2i000000000000000000
χ4644-4-4-444-4000000000004i−4i000000000000000-22-22−2i2i−2i2i000000000000000000
χ4744-4-4-444-400000000000−4i4i0000000000000002-22-2−2i2i−2i2i000000000000000000
χ4844-4-4-444-400000000000−4i4i000000000000000-22-222i−2i2i−2i000000000000000000
χ494-444-4-44-44400-4-40000000004-40000000000000000000000000000000000000
χ504-444-4-44-44400-4-4000000000-440000000000000000000000000000000000000
χ514-444-4-44-4-4-40044000000000004i−4i00000000000000000000000000000000000
χ524-444-4-44-4-4-4004400000000000−4i4i00000000000000000000000000000000000
χ534-44-4-44-444-4-444-4-4400-40040000000000000000000000000000000000000000
χ544-44-4-44-44-444-4-444-400-40040000000000000000000000000000000000000000
χ554-4-4444-4-4000000004i−4i0000000000000000002i−2i−2i2i2-2-22000000000000000000
χ564-4-4444-4-4000000004i−4i000000000000000000−2i2i2i−2i-222-2000000000000000000
χ574-4-4444-4-400000000−4i4i0000000000000000002i−2i−2i2i-222-2000000000000000000
χ584-4-4444-4-400000000−4i4i000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ594-4-4-44-444004-400-4400000000000000004-40000000000000000000000000000
χ604-4-4-44-444004-400-440000000000000000-440000000000000000000000000000
χ614-4-4-44-44400-44004-40000000000000000004-400000000000000000000000000
χ624-4-4-44-44400-44004-4000000000000000000-4400000000000000000000000000

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