Finite Group Databasebeta

← Group #280900

Character table — Group #280900

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222224444444444444888888888881616161616161616161616161616161616163232
order12222244444444444448888884444448888824444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-111-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-111111111-1-11-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-11-11111-1-111-1-1-1-111-1-11-1
χ61111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11-111-1-1-1-11111-1-111-11
χ71111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11-1-11111-1-1-1-1-1-111-11
χ81111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-111-1-1111111-1-11-1
χ91111111111111-1-1-1-1111111111111-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111-1-1-1-1111111111111-1-11-1-1-1-1-111-1-1-1-1-111-1-1111111-1-1
χ111111111111111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11-1-111111-1-111-1-11111-1-1
χ121111111111111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ131111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-111111-111-1-111-1-1-1-111-1-1111-1
χ141111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-11111-1-11-1-1-1111111-1-111-1-1-11
χ151111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1111111-1111-1-1-1-1-1-11111-1-1-11
χ161111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-11111-11-1-111-1-11111-1-1-1-1111-1
χ172222222-2-2222-20000-2-22222-2-2222200-200000-2-200000000000000000
χ182222222-2-2222-20000-2-22222-2-2-2-2-2-200-2000002200000000000000000
χ192222222-2-2222-20000-2-2-2-2-2-22222-2-2002000002-200000000000000000
χ202222222-2-2222-20000-2-2-2-2-2-222-2-22200200000-2200000000000000000
χ21222222-222-2-2-222222-2-20000000000-2-20000000000000002i−2i2i−2i000000
χ22222222-222-2-2-222222-2-20000000000-2-2000000000000000−2i2i−2i2i000000
χ23222222-222-2-2-22-2-2-2-2-2-20000000000220000000000000002i−2i−2i2i000000
χ24222222-222-2-2-22-2-2-2-2-2-2000000000022000000000000000−2i2i2i−2i000000
χ252222-2-22-2-2-2-2222i2i−2i−2i2-200000000002i−2i00000200-200002i−2i0000000000
χ262222-2-22-2-2-2-2222i2i−2i−2i2-200000000002i−2i00000-20020000−2i2i0000000000
χ272222-2-22-2-2-2-222−2i−2i2i2i2-20000000000−2i2i00000200-20000−2i2i0000000000
χ282222-2-22-2-2-2-222−2i−2i2i2i2-20000000000−2i2i00000-200200002i−2i0000000000
χ292222-2-2-22222-2-200002-222-2-222000000-2000000002i−2i2i−2i000000000000
χ302222-2-2-22222-2-200002-222-2-222000000-200000000−2i2i−2i2i000000000000
χ312222-2-2-22222-2-200002-2-2-222-2-20000002000000002i−2i−2i2i000000000000
χ322222-2-2-22222-2-200002-2-2-222-2-2000000200000000−2i2i2i−2i000000000000
χ332222-2-2-2-2-222-222i2i−2i−2i-2222-2-2-2-20000−2i2i22i2i−2i−2i00000000000000000000
χ342222-2-2-2-2-222-222i2i−2i−2i-22-2-222220000−2i2i-2−2i−2i2i2i00000000000000000000
χ352222-2-2-2-2-222-22−2i−2i2i2i-2222-2-2-2-200002i−2i2−2i−2i2i2i00000000000000000000
χ362222-2-2-2-2-222-22−2i−2i2i2i-22-2-2222200002i−2i-22i2i−2i−2i00000000000000000000
χ37444444-4-4-4-4-4-4-40000440000000000000000000000000000000000000
χ384444-4-4444-4-44-40000-440000000000000000000000000000000000000
χ394-44-40004i−4i00002+2i−2−2i2−2i−2+2i002i2−2i20022−2200000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ404-44-40004i−4i00002+2i−2−2i2−2i−2+2i00−2i22i200−22220000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ414-44-40004i−4i0000−2−2i2+2i−2+2i2−2i002i2−2i20022−220000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ424-44-40004i−4i0000−2−2i2+2i−2+2i2−2i00−2i22i200−222200000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ434-44-4000−4i4i00002−2i−2+2i2+2i−2−2i002i2−2i200−222200000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ444-44-4000−4i4i00002−2i−2+2i2+2i−2−2i00−2i22i20022−220000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ454-44-4000−4i4i0000−2+2i2−2i−2−2i2+2i002i2−2i200−22220000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ464-44-4000−4i4i0000−2+2i2−2i−2−2i2+2i00−2i22i20022−2200000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ474-4-444-44004-4-40000000000000000000000000000000000000022−220000
χ484-4-444-44004-4-400000000000000000000000000000000000000−22220000
χ494-4-444-4-400-4440000000000000004-4000000000000000000000000000
χ504-4-444-4-400-444000000000000000-44000000000000000000000000000
χ514-4-44-44400-44-400000000000004i−4i00000000000000000000000000000
χ524-4-44-44400-44-40000000000000−4i4i00000000000000000000000000000
χ534-4-44-44-4004-44000000000000000000000000000000000000000022−2200
χ544-4-44-44-4004-440000000000000000000000000000000000000000−222200
χ5588-8-80000000000000000042−42000000000000000000000000000000000
χ5688-8-800000000000000000−4242000000000000000000000000000000000

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