Finite Group Databasebeta

← Group #140331

Character table — Group #140331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222224444444448888888881616161616161616161616161616161632323232
order12224444444424488888881616161616161616444488888888161616164488
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ91111-1-11111-1-1-11-1-1-111-1-11iiii−i−i−i−iii−i−ii−i11-1-1i−i11-1-11-1i−i
χ101111-1-11111-1-1-11-1-1-111-1-11iiii−i−i−i−iii−i−i−ii11-1-1−ii-1-111-11−ii
χ111111-1-11111-1-1-11-1-1-111-1-11iiii−i−i−i−i−i−iiii−i-1-111i−i11-1-1-11−ii
χ121111-1-11111-1-1-11-1-1-111-1-11iiii−i−i−i−i−i−iii−ii-1-111−ii-1-1111-1i−i
χ131111-1-11111-1-1-11-1-1-111-1-11−i−i−i−iiiiiii−i−ii−i-1-111i−i-1-1111-1−ii
χ141111-1-11111-1-1-11-1-1-111-1-11−i−i−i−iiiiiii−i−i−ii-1-111−ii11-1-1-11i−i
χ151111-1-11111-1-1-11-1-1-111-1-11−i−i−i−iiiii−i−iiii−i11-1-1i−i-1-111-11i−i
χ161111-1-11111-1-1-11-1-1-111-1-11−i−i−i−iiiii−i−iii−ii11-1-1−ii11-1-11-1−ii
χ17222222222222222-2-2-2-2-2-2-2000000000000220000-2-200000000
χ18222222222222222-2-2-2-2-2-2-2000000000000-2-200002200000000
χ1922222222-2-222-2-2-222-2-2-2-22000000000000000000002i−2i2i−2i0000
χ2022222222-2-222-2-2-222-2-2-2-2200000000000000000000−2i2i−2i2i0000
χ2122222222-2-222-2-2-2-2-22222-222-2-222-2-200000000000000000000
χ2222222222-2-222-2-2-2-2-22222-2-2-222-2-22200000000000000000000
χ232222-2-22222-2-2-22-222-2-222-20000000000002i−2i0000−2i2i00000000
χ242222-2-22222-2-2-22-222-2-222-2000000000000−2i2i00002i−2i00000000
χ252222-2-222-2-2-2-22-222222-2-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000
χ262222-2-222-2-2-2-22-222222-2-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ272222-2-222-2-2-2-22-22-2-2-2-2222000000000000000000002i−2i−2i2i0000
χ282222-2-222-2-2-2-22-22-2-2-2-222200000000000000000000−2i2i2i−2i0000
χ292-22-22i−2i2-2002i−2i000002-22i−2i0002ζ3−2ζ3002ζ−2ζ1+i−1−i1−i−1+i00i2−i22−20000000000
χ302-22-22i−2i2-2002i−2i000002-22i−2i0002ζ3−2ζ3002ζ−2ζ−1−i1+i−1+i1−i00−i2i2−220000000000
χ312-22-22i−2i2-2002i−2i000002-22i−2i000−2ζ32ζ300−2ζ2ζ1+i−1−i1−i−1+i00−i2i2−220000000000
χ322-22-22i−2i2-2002i−2i000002-22i−2i000−2ζ32ζ300−2ζ2ζ−1−i1+i−1+i1−i00i2−i22−20000000000
χ332-22-2−2i2i2-200−2i2i000002-2−2i2i0002ζ−2ζ002ζ3−2ζ31−i−1+i1+i−1−i00i2−i2−220000000000
χ342-22-2−2i2i2-200−2i2i000002-2−2i2i0002ζ−2ζ002ζ3−2ζ3−1+i1−i−1−i1+i00−i2i22−20000000000
χ352-22-2−2i2i2-200−2i2i000002-2−2i2i000−2ζ2ζ00−2ζ32ζ31−i−1+i1+i−1−i00−i2i22−20000000000
χ362-22-2−2i2i2-200−2i2i000002-2−2i2i000−2ζ2ζ00−2ζ32ζ3−1+i1−i−1−i1+i00i2−i2−220000000000
χ37444444-4-444-4-44-4-400000000000000000000000000000000000
χ38444444-4-4-4-4-4-4-44400000000000000000000000000000000000
χ394444-4-4-4-44444-4-4400000000000000000000000000000000000
χ404444-4-4-4-4-4-44444-400000000000000000000000000000000000
χ414-44-44i−4i4-4004i−4i00000-44−4i4i00000000000000000000000000000
χ424-44-44i−4i-4400−4i4i00000000002+2i−2−2i002−2i−2+2i0000000000000000000000
χ434-44-44i−4i-4400−4i4i0000000000−2−2i2+2i00−2+2i2−2i0000000000000000000000
χ444-44-4−4i4i4-400−4i4i00000-444i−4i00000000000000000000000000000
χ454-44-4−4i4i-44004i−4i00000000002−2i−2+2i002+2i−2−2i0000000000000000000000
χ464-44-4−4i4i-44004i−4i0000000000−2+2i2−2i00−2−2i2+2i0000000000000000000000
χ4788-8-800008-80000000000000000000000000000000000000000
χ4888-8-80000-880000000000000000000000000000000000000000
χ498-8-88000000000004i2−4i2000000000000000000000000000000000
χ508-8-8800000000000−4i24i2000000000000000000000000000000000

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