Finite Group Databasebeta

← Group #98621

Character table — Group #98621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222244444444444422444444444488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1-1-111111111-111-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-111-1-111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-1-1
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
χ911111111-1-1-1-111-111-111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11111ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-111-111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11111−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-111-111-1-1-1-111-1-1-1-1111111iiii−i−i−i−i1-11-1-1-1−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-111-111-1-1-1-111-1-1-1-1111111−i−i−i−iiiii1-11-1-1-1ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-111-111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-11-11-1-1−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-111-111-111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-11-11-1-1ii−i−iii−i−i−i−iii
χ1511111111-1-1-1-111-111-111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-111ii−i−i−i−iii−i−iii
χ1611111111-1-1-1-111-111-111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-111−i−iiiii−i−iii−i−i
χ17222222222222222-2-2-2-2-2-22-2-20000000022-2-20000000000002-2000000000000
χ18222222222222222-2-2-2-2-2-22-2-200000000-2-222000000000000-22000000000000
χ19222222222222-2-2-2222-2-2-2-22-200220022000000000000-200-200000000000000
χ20222222222222-2-2-2222-2-2-2-22-200-2-200-2-2000000000000200200000000000000
χ21222222222222-2-2-2-2-2-2222-2-22220022000000000000000-2-2000000000000000
χ22222222222222-2-2-2-2-2-2222-2-22-2-200-2-200000000000000022000000000000000
χ2322222222-2-2-2-222-2-2-22-2-22-2220000000022-2-2000000000000-22000000000000
χ2422222222-2-2-2-222-2-2-22-2-22-22200000000-2-2220000000000002-2000000000000
χ2522222222-2-2-2-2-2-2222-2-2-222-22002200-2-2000000000000200-200000000000000
χ2622222222-2-2-2-2-2-2222-2-2-222-2200-2-20022000000000000-200200000000000000
χ2722222222-2-2-2-2-2-22-2-2222-222-22200-2-20000000000000002-2000000000000000
χ2822222222-2-2-2-2-2-22-2-2222-222-2-2-20022000000000000000-22000000000000000
χ292-22-2-222-222-2-20002-2-2000020002i−2i002i−2i000022−2−222−2−200000000000000i2−i2i2−i2
χ302-22-2-222-222-2-20002-2-2000020002i−2i002i−2i0000−2−222−2−22200000000000000−i2i2−i2i2
χ312-22-2-222-222-2-20002-2-200002000−2i2i00−2i2i000022−2−222−2−200000000000000−i2i2−i2i2
χ322-22-2-222-222-2-20002-2-200002000−2i2i00−2i2i0000−2−222−2−22200000000000000i2−i2i2−i2
χ332-22-2-222-2-2-2220002-220000-20002i−2i00−2i2i0000i2i2−i2−i2−i2−i2i2i200000000000000−222−2
χ342-22-2-222-2-2-2220002-220000-20002i−2i00−2i2i0000−i2−i2i2i2i2i2−i2−i2000000000000002−2−22
χ352-22-2-222-2-2-2220002-220000-2000−2i2i002i−2i0000i2i2−i2−i2−i2−i2i2i2000000000000002−2−22
χ362-22-2-222-2-2-2220002-220000-2000−2i2i002i−2i0000−i2−i2i2i2i2i2−i2−i200000000000000−222−2
χ372-2-22-22-222-22-20000002-2200-22-2002-2000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i20000
χ382-2-22-22-222-22-20000002-2200-22-2002-2000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i20000
χ392-2-22-22-222-22-20000002-2200-2-2200-22000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i20000
χ402-2-22-22-222-22-20000002-2200-2-2200-22000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i20000
χ412-2-22-22-22-22-220000002-2-20022-200-220000002−22−2−22−2200000000002−2−220000
χ422-2-22-22-22-22-220000002-2-20022-200-22000000−22−222−22−20000000000−222−20000
χ432-2-22-22-22-22-220000002-2-2002-22002-20000002−22−2−22−220000000000−222−20000
χ442-2-22-22-22-22-220000002-2-2002-22002-2000000−22−222−22−200000000002−2−220000
χ4544-4-444-4-44-4-440000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4644-4-444-4-44-4-44000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ4744-4-444-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ4844-4-444-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ494-4444-4-4-40000004000000-400000000000000000000000000002-22-200000000
χ504-4444-4-4-40000004000000-40000000000000000000000000000-22-2200000000
χ514-4444-4-4-4000000-4000000400000000000000000000000000002i−2i−2i2i00000000
χ524-4444-4-4-4000000-400000040000000000000000000000000000−2i2i2i−2i00000000
χ534-44-4-444-444-4-4000-4440000-4000000000000000000000000000000000000000
χ544-44-4-444-4-4-444000-44-400004000000000000000000000000000000000000000
χ554-4-44-44-444-44-4000000-44-400400000000000000000000000000000000000000
χ564-4-44-44-44-44-44000000-44400-400000000000000000000000000000000000000
χ574-4-4-44-44400004-4000000000000000000004-400000000000000000000000000
χ584-4-4-44-44400004-400000000000000000000-4400000000000000000000000000
χ594-4-4-44-4440000-440000000000000000004-40000000000000000000000000000
χ604-4-4-44-4440000-44000000000000000000-440000000000000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ6288-88-8-88-8000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).