Finite Group Databasebeta

← Group #125437

Character table — Group #125437

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
χ21222-22-2-2-2-2-2222i−2i000000002i−2i002-2002i−2i000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ22222-22-2-2-2-2-2222i−2i000000002i−2i002-2002i−2i00000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ23222-22-2-2-2-2-2222i−2i000000002i−2i00-2200−2i2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ24222-22-2-2-2-2-2222i−2i000000002i−2i00-2200−2i2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ25222-22-2-2-2-2-222−2i2i00000000−2i2i002-200−2i2i000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ26222-22-2-2-2-2-222−2i2i00000000−2i2i002-200−2i2i00000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ27222-22-2-2-2-2-222−2i2i00000000−2i2i00-22002i−2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ28222-22-2-2-2-2-222−2i2i00000000−2i2i00-22002i−2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ292-222-2-2-222-22-22i−2i00002i2i−2i−2i−2i2i2-2000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ302-222-2-2-222-22-22i−2i00002i2i−2i−2i−2i2i2-200000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ312-222-2-2-222-22-22i−2i0000−2i−2i2i2i−2i2i-2200000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ322-222-2-2-222-22-22i−2i0000−2i−2i2i2i−2i2i-220000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ332-222-2-2-222-22-2−2i2i00002i2i−2i−2i2i−2i-2200000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ342-222-2-2-222-22-2−2i2i00002i2i−2i−2i2i−2i-220000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ352-222-2-2-222-22-2−2i2i0000−2i−2i2i2i2i−2i2-2000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ362-222-2-2-222-22-2−2i2i0000−2i−2i2i2i2i−2i2-200000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3744444444-4-4-4-40044-4-400000000000000000000000000000000000000
χ3844444444-4-4-4-400-4-44400000000000000000000000000000000000000
χ39444-44-4-4-444-4-40000004-44-40000000000000000000000000000000000
χ40444-44-4-4-444-4-4000000-44-440000000000000000000000000000000000
χ4144-4-4-44-44000000004-40000000000000000002i−2i2i−2i0000000000000000
χ4244-4-4-44-44000000004-4000000000000000000−2i2i−2i2i0000000000000000
χ4344-4-4-44-4400000000-440000000000000000002i−2i−2i2i0000000000000000
χ4444-4-4-44-4400000000-44000000000000000000−2i2i2i−2i0000000000000000
χ454-444-4-4-44-44-4400000000000000004i−4i00000000000000000000000000
χ464-444-4-4-44-44-440000000000000000−4i4i00000000000000000000000000
χ474-44-4-444-44-4-440000004i−4i−4i4i0000000000000000000000000000000000
χ484-44-4-444-44-4-44000000−4i4i4i−4i0000000000000000000000000000000000
χ494-44-4-444-4-444-44400000000-4-400000000000000000000000000000000
χ504-44-4-444-4-444-4-4-4000000004400000000000000000000000000000000
χ514-4-4444-4-40000004i−4i00000000000000002-22i−2i00000000000000000000
χ524-4-4444-4-40000004i−4i0000000000000000-22−2i2i00000000000000000000
χ534-4-4444-4-4000000−4i4i00000000000000002-2−2i2i00000000000000000000
χ544-4-4444-4-4000000−4i4i0000000000000000-222i−2i00000000000000000000
χ5588-88-8-88-8000000000000000000000000000000000000000000000000
χ568-8-8-88-888000000000000000000000000000000000000000000000000

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