Finite Group Databasebeta

← Group #98686

Character table — Group #98686

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444422444444444488888888244444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-1-1
χ5111111111111111111111111-1-111-1-111-1-1-1-111111111-111-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ911111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-11-1111ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-11-1111−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111iiii−i−i−i−i-1-111-1-1−i−iii−i−iiiii−i−i
χ1211111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111−i−i−i−iiiii-1-111-1-1ii−i−iii−i−i−i−iii
χ1311111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i11-1-1-1-1−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii11-1-1-1-1ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-11-111ii−i−i−i−iii−i−iii
χ1611111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-11-111−i−iiiii−i−iii−i−i
χ17222222222222222-2-2-2-2-2-2-22-20000000022-2-20000000000002-2000000000000
χ18222222222222222-2-2-2-2-2-2-22-200000000-2-222000000000000-22000000000000
χ19222222222222-2-2-2222-2-2-2-2-22002200220000000000000-2-2000000000000000
χ20222222222222-2-2-2222-2-2-2-2-2200-2-200-2-2000000000000022000000000000000
χ21222222222222-2-2-2-2-2-22222-2-222002200000000000000-200-200000000000000
χ22222222222222-2-2-2-2-2-22222-2-2-2-200-2-200000000000000200200000000000000
χ2322222222-2-2-2-222-22-2-2-2-222-220000000022-2-2000000000000-22000000000000
χ2422222222-2-2-2-222-22-2-2-2-222-2200000000-2-2220000000000002-2000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-2222200-2-200000000000000200-200000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-222-2-2002200000000000000-200200000000000000
χ2722222222-2-2-2-2-2-22-222-2-2222-2002200-2-20000000000000-22000000000000000
χ2822222222-2-2-2-2-2-22-222-2-2222-200-2-2002200000000000002-2000000000000000
χ292-222-22-2-222-2-2000-22-2000002002i−2i002i−2i000022−2−222−2−20000000000i2−i2i2−i20000
χ302-222-22-2-222-2-2000-22-2000002002i−2i002i−2i0000−2−222−2−2220000000000−i2i2−i2i20000
χ312-222-22-2-222-2-2000-22-200000200−2i2i00−2i2i000022−2−222−2−20000000000−i2i2−i2i20000
χ322-222-22-2-222-2-2000-22-200000200−2i2i00−2i2i0000−2−222−2−2220000000000i2−i2i2−i20000
χ332-222-22-2-2-2-22200022-200000-2002i−2i00−2i2i0000i2i2−i2−i2−i2−i2i2i20000000000−222−20000
χ342-222-22-2-2-2-22200022-200000-2002i−2i00−2i2i0000−i2−i2i2i2i2i2−i2−i200000000002−2−220000
χ352-222-22-2-2-2-22200022-200000-200−2i2i002i−2i0000i2i2−i2−i2−i2−i2i2i200000000002−2−220000
χ362-222-22-2-2-2-22200022-200000-200−2i2i002i−2i0000−i2−i2i2i2i2i2−i2−i20000000000−222−20000
χ372-22-22-22-22i−2i2i−2i0000002-22i−2i002-2002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i
χ382-22-22-22-22i−2i2i−2i0000002-22i−2i002-2002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i
χ392-22-22-22-22i−2i2i−2i0000002-22i−2i00-2200−2i2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i
χ402-22-22-22-22i−2i2i−2i0000002-22i−2i00-2200−2i2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i
χ412-22-22-22-2−2i2i−2i2i0000002-2−2i2i002-200−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i
χ422-22-22-22-2−2i2i−2i2i0000002-2−2i2i002-200−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i
χ432-22-22-22-2−2i2i−2i2i0000002-2−2i2i00-22002i−2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i
χ442-22-22-22-2−2i2i−2i2i0000002-2−2i2i00-22002i−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i
χ45444-4-4-4-444i−4i−4i4i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000
χ46444-4-4-4-444i−4i−4i4i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ47444-4-4-4-44−4i4i4i−4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000
χ48444-4-4-4-44−4i4i4i−4i000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ4944-444-4-4-400000040000000-40000000000000000000000000002-22-200000000
χ5044-444-4-4-400000040000000-4000000000000000000000000000-22-2200000000
χ5144-444-4-4-4000000-4000000040000000000000000000000000002i−2i−2i2i00000000
χ5244-444-4-4-4000000-400000004000000000000000000000000000−2i2i2i−2i00000000
χ5344-4-4-444-400004-4000000000000000000004i−4i00000000000000000000000000
χ5444-4-4-444-400004-400000000000000000000−4i4i00000000000000000000000000
χ5544-4-4-444-40000-440000000000000000004i−4i0000000000000000000000000000
χ5644-4-4-444-40000-44000000000000000000−4i4i0000000000000000000000000000
χ574-444-44-4-444-4-40004-4400000-400000000000000000000000000000000000000
χ584-444-44-4-4-4-444000-4-4400000400000000000000000000000000000000000000
χ594-44-44-44-44i−4i4i−4i000000-44−4i4i0000000000000000000000000000000000000000
χ604-44-44-44-4−4i4i−4i4i000000-444i−4i0000000000000000000000000000000000000000
χ618-8-88-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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