Finite Group Databasebeta

← Group #98413

Character table — Group #98413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444222444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111-1-1-1-11111-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111111111-1-1-1-1
χ91111111111-111-1-1-1-1-1-1-11111111-1-1-1111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-111-1-1-1-1-1-1-11111111-1-1-1111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-111-1-1-1-1-1-1-111111-1-111-1-1-1-11-111ii−i−i−i−iiiii−i−i−i−iii
χ121111111111-111-1-1-1-1-1-1-111111-1-111-1-1-1-11-111−i−iiiii−i−i−i−iiiii−i−i
χ131111111111-111-1-1-1-1-1-1-11-1-1-1-111-1-11-1-11-1111ii−i−iii−i−i−i−iii−i−iii
χ141111111111-111-1-1-1-1-1-1-11-1-1-1-111-1-11-1-11-1111−i−iii−i−iiiii−i−iii−i−i
χ151111111111-111-1-1-1-1-1-1-11-1-1-1-1-1-111111-111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-111-1-1-1-1-1-1-11-1-1-1-1-1-111111-111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-2-222-2-22-2-222-2-20000-200002000000000000000000
χ1822222222222-2-2-222-2-22-2-2-2-222000020000-2000000000000000000
χ192222222222-2-2-22-2-222-22-222-2-2000020000-2000000000000000000
χ202222222222-2-2-22-2-222-22-2-2-2220000-200002000000000000000000
χ2122222222-2-22222-2-2-2-222-200002222000-2-20000000000000000000
χ2222222222-2-22222-2-2-2-222-20000-2-2-2-2000220000000000000000000
χ2322222222-2-22-2-2-2-2-2222-220000000002-20002-20000000000000000
χ2422222222-2-22-2-2-2-2-2222-22000000000-22000-220000000000000000
χ2522222222-2-2-222-22222-2-2-2000022-2-2000-220000000000000000000
χ2622222222-2-2-222-22222-2-2-20000-2-2220002-20000000000000000000
χ2722222222-2-2-2-2-2222-2-2-2220000000002-2000-220000000000000000
χ2822222222-2-2-2-2-2222-2-2-222000000000-220002-20000000000000000
χ292-2-2-22-2220022-220000-2-2000002-22-200000000i2−i2i2−i2i2−i2i2−i200000000
χ302-2-2-22-2220022-220000-2-2000002-22-200000000−i2i2−i2i2−i2i2−i2i200000000
χ312-2-2-22-2220022-220000-2-200000-22-2200000000i2−i2i2−i2−i2i2−i2i200000000
χ322-2-2-22-2220022-220000-2-200000-22-2200000000−i2i2−i2i2i2−i2i2−i200000000
χ332-2-2-22-22200-22-2-2000022000002-2-22000000002−2−222−2−2200000000
χ342-2-2-22-22200-22-2-2000022000002-2-2200000000−222−2−222−200000000
χ352-2-2-22-22200-22-2-200002200000-222-2000000002−2−22−222−200000000
χ362-2-2-22-22200-22-2-200002200000-222-200000000−222−22−2−2200000000
χ37444-4-4-44-4000000004i−4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ38444-4-4-44-4000000004i−4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ39444-4-4-44-400000000−4i4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ40444-4-4-44-400000000−4i4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4144-44-4-4-444-400000000000004i−4i0000000000000000000000000000
χ4244-44-4-4-444-40000000000000−4i4i0000000000000000000000000000
χ4344-44-4-4-44-44000000000004i−4i000000000000000000000000000000
χ4444-44-4-4-44-4400000000000−4i4i000000000000000000000000000000
χ4544-4-444-4-40000004i−4i0000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ4644-4-444-4-40000004i−4i000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ4744-4-444-4-4000000−4i4i0000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ4844-4-444-4-4000000−4i4i000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ494-4-4-44-444004-44-40000-44000000000000000000000000000000000
χ504-4-4-44-44400-4-44400004-4000000000000000000000000000000000
χ518-8888-8-8-8000000000000000000000000000000000000000000000
χ528-88-8-88-88000000000000000000000000000000000000000000000
χ538-8-88-888-8000000000000000000000000000000000000000000000

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