Finite Group Databasebeta

← Group #125396

Character table — Group #125396

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-222-2-2-2-222-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000
χ19222222222222-2-222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000
χ21222-2-2-22-22-22-20000002i2i−2i−2i00002i−2i2-20000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ22222-2-2-22-22-22-20000002i2i−2i−2i00002i−2i2-2000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ23222-2-2-22-22-22-20000002i2i−2i−2i0000−2i2i-220000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ24222-2-2-22-22-22-20000002i2i−2i−2i0000−2i2i-22000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ25222-2-2-22-22-22-2000000−2i−2i2i2i00002i−2i-220000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ26222-2-2-22-22-22-2000000−2i−2i2i2i00002i−2i-22000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ27222-2-2-22-22-22-2000000−2i−2i2i2i0000−2i2i2-20000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ28222-2-2-22-22-22-2000000−2i−2i2i2i0000−2i2i2-2000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ292-2-222-22-2-222-22i−2i00002i−2i2i−2i2i−2i2-20000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ302-2-222-22-2-222-22i−2i00002i−2i2i−2i2i−2i2-2000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ312-2-222-22-2-222-22i−2i0000−2i2i−2i2i2i−2i-22000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ322-2-222-22-2-222-22i−2i0000−2i2i−2i2i2i−2i-2200000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ332-2-222-22-2-222-2−2i2i00002i−2i2i−2i−2i2i-22000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ342-2-222-22-2-222-2−2i2i00002i−2i2i−2i−2i2i-2200000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ352-2-222-22-2-222-2−2i2i0000−2i2i−2i2i−2i2i2-20000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ362-2-222-22-2-222-2−2i2i0000−2i2i−2i2i−2i2i2-2000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ3744444444-4-4-4-40044-4-400000000000000000000000000000000000000
χ3844444444-4-4-4-400-4-44400000000000000000000000000000000000000
χ39444-4-4-44-4-44-444400000000-4-400000000000000000000000000000000
χ40444-4-4-44-4-44-44-4-4000000004400000000000000000000000000000000
χ4144-44-4-4-44000000004i−4i0000000000000000002i−2i2-20000000000000000
χ4244-44-4-4-44000000004i−4i000000000000000000−2i2i-220000000000000000
χ4344-44-4-4-4400000000−4i4i0000000000000000002i−2i-220000000000000000
χ4444-44-4-4-4400000000−4i4i000000000000000000−2i2i2-20000000000000000
χ454-44-44-4-440000004i−4i00000000000000002i−2i2-200000000000000000000
χ464-44-44-4-440000004i−4i0000000000000000−2i2i-2200000000000000000000
χ474-44-44-4-44000000−4i4i00000000000000002i−2i-2200000000000000000000
χ484-44-44-4-44000000−4i4i0000000000000000−2i2i2-200000000000000000000
χ494-4-444-44-44-4-440000000000000000004i−4i000000000000000000000000
χ504-4-444-44-44-4-44000000000000000000−4i4i000000000000000000000000
χ514-4-4-4-444444-4-44i−4i00000000−4i4i00000000000000000000000000000000
χ524-4-4-4-444444-4-4−4i4i000000004i−4i00000000000000000000000000000000
χ534-4-4-4-4444-4-4440000004-4-440000000000000000000000000000000000
χ544-4-4-4-4444-4-444000000-444-40000000000000000000000000000000000
χ5588-8-888-8-8000000000000000000000000000000000000000000000000
χ568-888-88-8-8000000000000000000000000000000000000000000000000

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