Finite Group Databasebeta

← Group #98586

Character table — Group #98586

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444422444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11111
χ911111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−i-11111-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii-11111-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111iiii−i−i−i−i1-11-1-1-1ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111−i−i−i−iiiii1-11-1-1-1−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-11-1-1-11−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-11-1-1-11ii−i−iii−i−i−i−iii
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1iiii−i−i−i−i1-1-1111−i−iiiii−i−i−i−iii
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1−i−i−i−iiiii1-1-1111ii−i−i−i−iiiii−i−i
χ1722222222222222-2-2-2-222-2-2-2-200002222000000000000-2-20000000000000000
χ1822222222222222-2-2-2-222-2-2-2-20000-2-2-2-2000000000000220000000000000000
χ19222222222222-2-222-2-2-2-2-2-2222222000000000000000000-200-2000000000000
χ20222222222222-2-222-2-2-2-2-2-222-2-2-2-20000000000000000002002000000000000
χ21222222222222-2-2-2-222-2-222-2-20000000022-2-2000000000002-20000000000000
χ22222222222222-2-2-2-222-2-222-2-200000000-2-22200000000000-220000000000000
χ2322222222-2-2-2-22222-2-2-2-222-2-222-2-2000000000000000000-2002000000000000
χ2422222222-2-2-2-22222-2-2-2-222-2-2-2-222000000000000000000200-2000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-2220000000022-2-200000000000-220000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-22200000000-2-222000000000002-20000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000022-2-20000000000002-20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222220000-2-222000000000000-220000000000000000
χ292-222-2-2-222i−2i2i−2i002-20000002i−2i2-22i−2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000001+i−1−i1−i−1+i00000000
χ302-222-2-2-222i−2i2i−2i002-20000002i−2i2-22i−2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000−1−i1+i−1+i1−i00000000
χ312-222-2-2-222i−2i2i−2i002-20000002i−2i-22−2i2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000−1−i1+i−1+i1−i00000000
χ322-222-2-2-222i−2i2i−2i002-20000002i−2i-22−2i2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000001+i−1−i1−i−1+i00000000
χ332-222-2-2-22−2i2i−2i2i002-2000000−2i2i2-2−2i2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000001−i−1+i1+i−1−i00000000
χ342-222-2-2-22−2i2i−2i2i002-2000000−2i2i2-2−2i2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000−1+i1−i−1−i1+i00000000
χ352-222-2-2-22−2i2i−2i2i002-2000000−2i2i-222i−2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000−1+i1−i−1−i1+i00000000
χ362-222-2-2-22−2i2i−2i2i002-2000000−2i2i-222i−2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000001−i−1+i1+i−1−i00000000
χ372-2-2-2-222222-2-22-200002-2000000002-22-20000i2−i2i2−i2i2−i2i2−i200000000000000i2−i2i2−i2
χ382-2-2-2-222222-2-22-200002-2000000002-22-20000−i2i2−i2i2−i2i2−i2i200000000000000−i2i2−i2i2
χ392-2-2-2-222222-2-22-200002-200000000-22-220000i2−i2i2−i2i2−i2i2−i200000000000000−i2i2−i2i2
χ402-2-2-2-222222-2-22-200002-200000000-22-220000−i2i2−i2i2−i2i2−i2i200000000000000i2−i2i2−i2
χ412-2-2-2-2222-2-222-2200002-2000000002-2-2200002−22−2−22−22000000000000002−2−22
χ422-2-2-2-2222-2-222-2200002-2000000002-2-220000−22−222−22−200000000000000−222−2
χ432-2-2-2-2222-2-222-2200002-200000000-222-200002−22−2−22−2200000000000000−222−2
χ442-2-2-2-2222-2-222-2200002-200000000-222-20000−22−222−22−2000000000000002−2−22
χ4544-4-44-4-444i−4i−4i4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ4644-4-44-4-444i−4i−4i4i000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000
χ4744-4-44-4-44−4i4i4i−4i0000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ4844-4-44-4-44−4i4i4i−4i000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000
χ494-444-4-4-444i−4i4i−4i00-44000000−4i4i00000000000000000000000000000000000000
χ504-444-4-4-44−4i4i−4i4i00-440000004i−4i00000000000000000000000000000000000000
χ514-44-444-4-4000000004-400000000000000004i−4i00000000000000000000000000
χ524-44-444-4-4000000004-40000000000000000−4i4i00000000000000000000000000
χ534-44-444-4-400000000-44000000000000004i−4i0000000000000000000000000000
χ544-44-444-4-400000000-4400000000000000−4i4i0000000000000000000000000000
χ554-4-444-44-40000000000004i−4i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ564-4-444-44-40000000000004i−4i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ574-4-444-44-4000000000000−4i4i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ584-4-444-44-4000000000000−4i4i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ594-4-4-4-444444-4-4-440000-44000000000000000000000000000000000000000000
χ604-4-4-4-4444-4-4444-40000-44000000000000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-88-88-8-8000000000000000000000000000000000000000000000000000000

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