Finite Group Databasebeta

← Group #150350

Character table — Group #150350

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224444444444444444448888888844448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-222-2-20000000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2220000000000000000000000000000
χ192222-2-2-2-222-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000
χ202222-2-2-2-222-2-2-2-222-2-222-2-22222-2-20000000000000000000000000000
χ212-22-22i2i−2i−2i2-22i−2i2i−2i2-2002i−2i0000002-2000000000000i2−i22−22−2i2−i200000000
χ222-22-22i2i−2i−2i2-22i−2i2i−2i2-2002i−2i0000002-2000000000000−i2i2−22−22−i2i200000000
χ232-22-22i2i−2i−2i2-22i−2i2i−2i2-200−2i2i000000-220000000000002−2−i2i2i2−i2−2200000000
χ242-22-22i2i−2i−2i2-22i−2i2i−2i2-200−2i2i000000-22000000000000−22i2−i2−i2i22−200000000
χ252-22-22i2i−2i−2i2-22i−2i−2i2i-222-20000002i−2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ262-22-22i2i−2i−2i2-22i−2i−2i2i-222-20000002i−2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ272-22-22i2i−2i−2i2-22i−2i−2i2i-22-22000000−2i2i00000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ282-22-22i2i−2i−2i2-22i−2i−2i2i-22-22000000−2i2i0000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ292-22-2−2i−2i2i2i2-2−2i2i2i−2i-222-2000000−2i2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ302-22-2−2i−2i2i2i2-2−2i2i2i−2i-222-2000000−2i2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ312-22-2−2i−2i2i2i2-2−2i2i2i−2i-22-220000002i−2i00000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ322-22-2−2i−2i2i2i2-2−2i2i2i−2i-22-220000002i−2i0000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ332-22-2−2i−2i2i2i2-2−2i2i−2i2i2-2002i−2i000000-220000000000002−2i2−i2−i2i2−2200000000
χ342-22-2−2i−2i2i2i2-2−2i2i−2i2i2-2002i−2i000000-22000000000000−22−i2i2i2−i22−200000000
χ352-22-2−2i−2i2i2i2-2−2i2i−2i2i2-200−2i2i0000002-2000000000000i2−i2−22−22i2−i200000000
χ362-22-2−2i−2i2i2i2-2−2i2i−2i2i2-200−2i2i0000002-2000000000000−i2i22−22−2−i2i200000000
χ37444444444444-4-4-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-400000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ3944444444-4-4-4-40000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ404444-4-4-4-444-4-444-4-40000000000000000000000000000000000000000
χ414444-4-4-4-4-4-44400000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ424444-4-4-4-4-4-4440000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ434-44-44i4i−4i−4i-44−4i4i0000000000000000000000002-22i−2i0000000000000000
χ444-44-44i4i−4i−4i-44−4i4i000000000000000000000000-22−2i2i0000000000000000
χ454-44-4−4i−4i4i4i-444i−4i0000000000000000000000002-2−2i2i0000000000000000
χ464-44-4−4i−4i4i4i-444i−4i000000000000000000000000-222i−2i0000000000000000
χ474-4-444i−4i4i−4i0000000000002i−2i2-200002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ00000000000000000000
χ484-4-444i−4i4i−4i0000000000002i−2i2-20000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ00000000000000000000
χ494-4-444i−4i4i−4i000000000000−2i2i-2200002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000000000000000
χ504-4-444i−4i4i−4i000000000000−2i2i-220000−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ300000000000000000000
χ514-4-44−4i4i−4i4i0000000000002i−2i-2200002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ00000000000000000000
χ524-4-44−4i4i−4i4i0000000000002i−2i-220000−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ00000000000000000000
χ534-4-44−4i4i−4i4i000000000000−2i2i2-200002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ300000000000000000000
χ544-4-44−4i4i−4i4i000000000000−2i2i2-20000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ300000000000000000000
χ5588-8-88-8-88000000000000000000000000000000000000000000000000
χ5688-8-8-888-8000000000000000000000000000000000000000000000000

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