Finite Group Databasebeta

← Group #131213

Character table — Group #131213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order12222244444444444422444424444444444444444488888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1111111-1-1-11-1-11-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-1111111-1-1-11-1-11-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-1111111-1-1-1-11-1-11-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-1111111-1-1-1-11-1-11-1-111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-1111111-1-1-1-111-1-1-1111-1-11-11-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-1111111-1-1-1-111-1-1-1111-1-11-11-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1111-11-11ii−i−iii−i−i−i−iii−i−iii
χ12111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1111-11-11−i−iii−i−iiiii−i−iii−i−i
χ13111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-111-1-11ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1-1-111-1-1-1-1-1-1-1-111111-11-11-1-111-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-111-1-1-1-1-1-1-1-111111-11-11-1-111-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-222-200-20000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-2-2-220020000000000000000000000
χ192222222222-2-20000-2-22-22-20000200200-2-20000000000000000
χ202222222222-2-20000-2-22-22-20000-200-200220000000000000000
χ212222222222-2-20000-2-2-22-2200020020-2-2000000000000000000
χ222222222222-2-20000-2-2-22-22000-200-2022000000000000000000
χ23222222-2-2-2-2222222-2-222-2-2-2-2200-20000000000000000000000
χ24222222-2-2-2-222-2-2-2-2-2-222-2-222-20020000000000000000000000
χ25222222-2-2-2-2-2-20000222-2-22000200-20-22000000000000000000
χ26222222-2-2-2-2-2-20000222-2-22000-200202-2000000000000000000
χ27222222-2-2-2-2-2-2000022-222-20000200-200-220000000000000000
χ28222222-2-2-2-2-2-2000022-222-20000-2002002-20000000000000000
χ292-22-22-22i−2i2i−2i2-222-2-22i−2i00002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ302-22-22-22i−2i2i−2i2-222-2-22i−2i00002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ312-22-22-22i−2i2i−2i2-2-2-2222i−2i0000−2i2i00000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ322-22-22-22i−2i2i−2i2-2-2-2222i−2i0000−2i2i0000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ332-22-22-2−2i2i−2i2i2-222-2-2−2i2i0000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ342-22-22-2−2i2i−2i2i2-222-2-2−2i2i0000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ352-22-22-2−2i2i−2i2i2-2-2-222−2i2i00002i−2i00000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ362-22-22-2−2i2i−2i2i2-2-2-222−2i2i00002i−2i0000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ374444-4-444-4-4000000000000000000000000000000002i−2i2i−2i0000
χ384444-4-444-4-400000000000000000000000000000000−2i2i−2i2i0000
χ394444-4-4-4-444000000000000000000000000000000002-2-220000
χ404444-4-4-4-44400000000000000000000000000000000-222-20000
χ414-44-44-44i−4i4i−4i-440000−4i4i00000000000000000000000000000000
χ424-44-44-4−4i4i−4i4i-4400004i−4i00000000000000000000000000000000
χ434-44-4-444i−4i−4i4i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ444-44-4-444i−4i−4i4i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ454-44-4-44−4i4i4i−4i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ464-44-4-44−4i4i4i−4i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ4788-8-8000000004-44-40000000000000000000000000000000000
χ4888-8-800000000-44-440000000000000000000000000000000000
χ498-8-88000000004-4-440000000000000000000000000000000000
χ508-8-8800000000-444-40000000000000000000000000000000000

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