Finite Group Databasebeta

← Group #102449

Character table — Group #102449

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222222222444488888888888888888888888888161616161616161632323232
order12222222222244444444444444444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ922222222222222222222-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000
χ1022222222222222222222-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000
χ11222222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-20000000000000000000000000000
χ12222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000
χ13222222222222-2-2-2-2-2-2-2-2-2-2-2-22200000000000000002i2i2i2i−2i−2i−2i−2i000000000000
χ14222222222222-2-2-2-2-2-2-2-2-2-2-2-2220000000000000000−2i−2i−2i−2i2i2i2i2i000000000000
χ1522222222-2-2-2-222-2-222-2-22-22-22-2000000000000000000000000000000002-200
χ1622222222-2-2-2-222-2-222-2-22-22-22-200000000000000000000000000000000-2200
χ1722222222-2-2-2-222-2-222-2-2-22-22-2200000000000000000000000000000000002-2
χ1822222222-2-2-2-222-2-222-2-2-22-22-220000000000000000000000000000000000-22
χ1922222222-2-2-2-2-2-222-2-2222-22-2-2200000000000000000000000022-2-200000000
χ2022222222-2-2-2-2-2-222-2-2222-22-2-22000000000000000000000000-2-22200000000
χ2122222222-2-2-2-2-2-222-2-222-22-222-2000000000000000000000000000022-2-20000
χ2222222222-2-2-2-2-2-222-2-222-22-222-20000000000000000000000000000-2-2220000
χ2322-222-2-2-222-2-2000000002-2-220000002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ2422-222-2-2-222-2-2000000002-2-220000002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ2522-222-2-2-222-2-2000000002-2-22000000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ2622-222-2-2-222-2-2000000002-2-22000000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ2722-222-2-2-222-2-200000000-222-20022-2-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2822-222-2-2-222-2-200000000-222-20022-2-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2922-222-2-2-222-2-200000000-222-200-2-2220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3022-222-2-2-222-2-200000000-222-200-2-2220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ312-2-22-22-222-22-22-2222-2-2-20000000000000000002-22-200000000i2−i2i2−i2i2−i2i2−i20000
χ322-2-22-22-222-22-22-2222-2-2-20000000000000000002-22-200000000−i2i2−i2i2−i2i2−i2i20000
χ332-2-22-22-222-22-22-2222-2-2-2000000000000000000-22-2200000000i2−i2i2−i2−i2i2−i2i20000
χ342-2-22-22-222-22-22-2222-2-2-2000000000000000000-22-2200000000−i2i2−i2i2i2−i2i2−i20000
χ352-2-22-22-22-22-22-2222-22-2-2000000000000002-22-2000000000000i2−i2−i2i2i2−i2−i2i20000
χ362-2-22-22-22-22-22-2222-22-2-2000000000000002-22-2000000000000−i2i2i2−i2−i2i2i2−i20000
χ372-2-22-22-22-22-22-2222-22-2-200000000000000-22-22000000000000i2−i2−i2i2−i2i2i2−i20000
χ382-2-22-22-22-22-22-2222-22-2-200000000000000-22-22000000000000−i2i2i2−i2i2−i2−i2i20000
χ39444-4-4-4-4400004-400-44000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ40444-4-4-4-4400004-400-4400000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ41444-4-4-4-440000-44004-4000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ42444-4-4-4-440000-44004-400000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ4344-444-4-4-4-4-4440000000044-4-400000000000000000000000000000000000000
χ4444-444-4-4-4-4-44400000000-4-44400000000000000000000000000000000000000
χ4544-4-4-444-40000004i−4i004i−4i0000002i−2i−2i2i2-2-220000000000000000000000000000
χ4644-4-4-444-40000004i−4i004i−4i000000−2i2i2i−2i-222-20000000000000000000000000000
χ4744-4-4-444-4000000−4i4i00−4i4i0000002i−2i−2i2i-222-20000000000000000000000000000
χ4844-4-4-444-4000000−4i4i00−4i4i000000−2i2i2i−2i2-2-220000000000000000000000000000
χ494-444-4-44-44-4-44000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ504-444-4-44-44-4-4400000000000000000000000000−2i22i22i2−2i200000000000000000000
χ514-444-4-44-4-444-400000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ524-444-4-44-4-444-40000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ534-44-444-4-40000004i−4i00−4i4i00000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ544-44-444-4-40000004i−4i00−4i4i0000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ554-44-444-4-4000000−4i4i004i−4i00000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ564-44-444-4-4000000−4i4i004i−4i0000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ574-4-44-44-444-44-4-44-4-4-4444000000000000000000000000000000000000000000
χ584-4-44-44-44-44-444-4-4-44-444000000000000000000000000000000000000000000
χ594-4-4-44-44400004400-4-40000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ604-4-4-44-44400004400-4-4000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ614-4-4-44-4440000-4-400440000000000000000000000002-2-22-222-2000000000000
χ624-4-4-44-4440000-4-40044000000000000000000000000-222-22-2-22000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.