Finite Group Databasebeta

← Group #98628

Character table — Group #98628

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
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-1-1
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
χ911111111-1-1-1-111-11111-1-1-1-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−i1-11-111ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-11111-1-1-1-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii1-11-111−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-11111-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i-1-111-1-1−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-11111-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiii-1-111-1-1ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-11111-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−i11-1-1-1-1−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-111-11111-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiii11-1-1-1-1ii−i−iii−i−i−i−iii
χ1511111111-1-1-1-111-11111-1-1-1-1-1-1-111-1-111-1-1-1-1iiii−i−i−i−i-11-1111ii−i−i−i−iii−i−iii
χ1611111111-1-1-1-111-11111-1-1-1-1-1-1-111-1-111-1-1-1-1−i−i−i−iiiii-11-1111−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
χ19222222222222-2-2-222-2-22-2-22-200002222000000000000-200-200000000000000
χ20222222222222-2-2-222-2-22-2-22-20000-2-2-2-2000000000000200200000000000000
χ21222222222222-2-2-2-2-222-22-2-22222200000000000000000-2-2000000000000000
χ22222222222222-2-2-2-2-222-22-2-22-2-2-2-20000000000000000022000000000000000
χ2322222222-2-2-2-222-2-2-2-2-222-2220000000022-2-2000000000000-22000000000000
χ2422222222-2-2-2-222-2-2-2-2-222-22200000000-2-2220000000000002-2000000000000
χ2522222222-2-2-2-2-2-2222-2-2-222-22000022-2-2000000000000-200200000000000000
χ2622222222-2-2-2-2-2-2222-2-2-222-220000-2-222000000000000200-200000000000000
χ2722222222-2-2-2-2-2-22-2-2222-222-222-2-2000000000000000002-2000000000000000
χ2822222222-2-2-2-2-2-22-2-2222-222-2-2-22200000000000000000-22000000000000000
χ292-22-222-2-222-2-20002-200-2002000002i−2i2i−2i000022−2−222−2−200000000000000i2−i2i2−i2
χ302-22-222-2-222-2-20002-200-2002000002i−2i2i−2i0000−2−222−2−22200000000000000−i2i2−i2i2
χ312-22-222-2-222-2-20002-200-200200000−2i2i−2i2i000022−2−222−2−200000000000000−i2i2−i2i2
χ322-22-222-2-222-2-20002-200-200200000−2i2i−2i2i0000−2−222−2−22200000000000000i2−i2i2−i2
χ332-22-222-2-2-2-2220002-200200-2000002i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i200000000000000−222−2
χ342-22-222-2-2-2-2220002-200200-2000002i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2000000000000002−2−22
χ352-22-222-2-2-2-2220002-200200-200000−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2000000000000002−2−22
χ362-22-222-2-2-2-2220002-200200-200000−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i200000000000000−222−2
χ372-2-2-22-2222-22-2000002-20200-22-22-200000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i20000
χ382-2-2-22-2222-22-2000002-20200-22-22-200000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i20000
χ392-2-2-22-2222-22-2000002-20200-2-22-2200000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i20000
χ402-2-2-22-2222-22-2000002-20200-2-22-2200000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i20000
χ412-2-2-22-222-22-22000002-20-20022-2-22000000002−22−2−22−2200000000002−2−220000
χ422-2-2-22-222-22-22000002-20-20022-2-2200000000−22−222−22−20000000000−222−20000
χ432-2-2-22-222-22-22000002-20-2002-222-2000000002−22−2−22−220000000000−222−20000
χ442-2-2-22-222-22-22000002-20-2002-222-200000000−22−222−22−200000000002−2−220000
χ4544-444-4-4-44-4-440000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4644-444-4-4-44-4-44000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ4744-444-4-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ4844-444-4-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ494-444-4-4-440000004000000-400000000000000000000000000002i−2i2i−2i00000000
χ504-444-4-4-440000004000000-40000000000000000000000000000−2i2i−2i2i00000000
χ514-444-4-4-44000000-4000000400000000000000000000000000002-2-2200000000
χ524-444-4-4-44000000-400000040000000000000000000000000000-222-200000000
χ534-44-444-4-444-4-4000-4400400-4000000000000000000000000000000000000000
χ544-44-444-4-4-4-444000-4400-4004000000000000000000000000000000000000000
χ554-4-44-444-400004-4000000000000000000004i−4i00000000000000000000000000
χ564-4-44-444-400004-400000000000000000000−4i4i00000000000000000000000000
χ574-4-44-444-40000-440000000000000000004i−4i0000000000000000000000000000
χ584-4-44-444-40000-44000000000000000000−4i4i0000000000000000000000000000
χ594-4-4-44-4444-44-400000-440-400400000000000000000000000000000000000000
χ604-4-4-44-444-44-4400000-440400-400000000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-8-8-88-88000000000000000000000000000000000000000000000000000000

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