Finite Group Databasebeta

← Group #98577

Character table — Group #98577

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1-1-1111111111-11-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-111-1-1-1-1-1-11111111111-11-11-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ911111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1iiii−i−i−i−i-1-111-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1−i−i−i−iiiii-1-111-1-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111iiii−i−i−i−i-111-111ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111−i−i−i−iiiii-111-111−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i1-1-1111−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii1-1-1111ii−i−iii−i−i−i−iii
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i11-1-1-1-1−i−iiiii−i−i−i−iii
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii11-1-1-1-1ii−i−i−i−iiiii−i−i
χ172222222222222222-2-2-2-2-2-2-2-2002200000022000000000-20-200000000000000
χ182222222222222222-2-2-2-2-2-2-2-200-2-2000000-2-200000000020200000000000000
χ19222222222222-2-2-2-222-2-2-2-22200000022-2-2000000000000002-2000000000000
χ20222222222222-2-2-2-222-2-2-2-222000000-2-22200000000000000-22000000000000
χ21222222222222-2-2-2-2-2-22222-2-222002200000000000000-20-2000000000000000
χ22222222222222-2-2-2-2-2-22222-2-2-2-200-2-200000000000000202000000000000000
χ2322222222-2-2-2-222-2-222-2-222-2-200000022-2-200000000000000-22000000000000
χ2422222222-2-2-2-222-2-222-2-222-2-2000000-2-222000000000000002-2000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-2222200-2-20000000000000020-2000000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-222-2-2002200000000000000-202000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-222220022000000-2-200000000020-200000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2222200-2-200000022000000000-20200000000000000
χ29222-2-2-2-222i−2i2i−2i0000002-22i−2i002-2002i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000001+i−1−i1−i−1+i00000000
χ30222-2-2-2-222i−2i2i−2i0000002-22i−2i002-2002i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000−1−i1+i−1+i1−i00000000
χ31222-2-2-2-222i−2i2i−2i0000002-22i−2i00-2200−2i2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000−1−i1+i−1+i1−i00000000
χ32222-2-2-2-222i−2i2i−2i0000002-22i−2i00-2200−2i2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000001+i−1−i1−i−1+i00000000
χ33222-2-2-2-22−2i2i−2i2i0000002-2−2i2i002-200−2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000001−i−1+i1+i−1−i00000000
χ34222-2-2-2-22−2i2i−2i2i0000002-2−2i2i002-200−2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000−1+i1−i−1−i1+i00000000
χ35222-2-2-2-22−2i2i−2i2i0000002-2−2i2i00-22002i−2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000−1+i1−i−1−i1+i00000000
χ36222-2-2-2-22−2i2i−2i2i0000002-2−2i2i00-22002i−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000001−i−1+i1+i−1−i00000000
χ372-22-222-2-222-2-2-222-200000000002i−2i0000002i−2i2−22−22−22−200000000000000i2−i2i2−i2
χ382-22-222-2-222-2-2-222-200000000002i−2i0000002i−2i−22−22−22−2200000000000000−i2i2−i2i2
χ392-22-222-2-222-2-2-222-20000000000−2i2i000000−2i2i2−22−22−22−200000000000000−i2i2−i2i2
χ402-22-222-2-222-2-2-222-20000000000−2i2i000000−2i2i−22−22−22−2200000000000000i2−i2i2−i2
χ412-22-222-2-2-2-2222-22-200000000002i−2i000000−2i2ii2−i2i2−i2−i2i2−i2i200000000000000−222−2
χ422-22-222-2-2-2-2222-22-200000000002i−2i000000−2i2i−i2i2−i2i2i2−i2i2−i2000000000000002−2−22
χ432-22-222-2-2-2-2222-22-20000000000−2i2i0000002i−2ii2−i2i2−i2−i2i2−i2i2000000000000002−2−22
χ442-22-222-2-2-2-2222-22-20000000000−2i2i0000002i−2i−i2i2−i2i2i2−i2i2−i200000000000000−222−2
χ45444-4-4-4-444i−4i4i−4i000000-44−4i4i0000000000000000000000000000000000000000
χ46444-4-4-4-44−4i4i−4i4i000000-444i−4i0000000000000000000000000000000000000000
χ4744-4-44-44-4000000000000004i−4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4844-4-44-44-4000000000000004i−4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ4944-4-44-44-400000000000000−4i4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ5044-4-44-44-400000000000000−4i4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ514-444-4-44-44i−4i−4i4i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000
χ524-444-4-44-44i−4i−4i4i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ534-444-4-44-4−4i4i4i−4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000
χ544-444-4-44-4−4i4i4i−4i000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ554-44-444-4-444-4-44-4-440000000000000000000000000000000000000000000000
χ564-44-444-4-4-4-444-44-440000000000000000000000000000000000000000000000
χ574-4-4-4-4444000000004-4000000000000004-40000000000000000000000000000
χ584-4-4-4-4444000000004-400000000000000-440000000000000000000000000000
χ594-4-4-4-444400000000-440000000000004-4000000000000000000000000000000
χ604-4-4-4-444400000000-44000000000000-44000000000000000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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