Finite Group Databasebeta

← Group #169621

Character table — Group #169621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222222244444444444422224444888888888888888824444444888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111-1-1-1-111-1-1-1-11-1-111111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-11-1
χ1011111111-1-1-1-111-1-1-1-11-1-111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111-11
χ1111111111-1-1-1-111-1-1-1-11-1-111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-11
χ1211111111-1-1-1-111-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-11-1
χ1311111111-1-1-1-111-1-1-1-11-1-1111-1-11111-1-11111-1-1-1-1-1-1-1-111111-11-1-11-1111-1-1-11
χ1411111111-1-1-1-111-1-1-1-11-1-1111-1-11111-1-1-1-1-1-111111111-1-1-1-11-11-1-11-11-1-1111-1
χ1511111111-1-1-1-111-1-1-1-11-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1111-11-1-1-1111-1
χ1611111111-1-1-1-111-1-1-1-11-1-1111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1111-11-111-1-1-11
χ172222222222222-222-2-2-2-2-22-2-200000000000000000000000000002-2-22000000
χ182222222222222-222-2-2-2-2-22-2-20000000000000000000000000000-222-2000000
χ19222222222222-22-2-222-2-2-2-22-2000022220000000000000000-200-20000000000
χ20222222222222-22-2-222-2-2-2-22-20000-2-2-2-2000000000000000020020000000000
χ21222222222222-2-2-2-2-2-2222-2-222222000000000000000000000-2-200000000000
χ22222222222222-2-2-2-2-2-2222-2-22-2-2-2-20000000000000000000002200000000000
χ2322222222-2-2-2-22-2-2-222-2222-2-2000000000000000000000000000022-2-2000000
χ2422222222-2-2-2-22-2-2-222-2222-2-20000000000000000000000000000-2-222000000
χ2522222222-2-2-2-2-2222-2-2-222-22-2000022-2-20000000000000000-20020000000000
χ2622222222-2-2-2-2-2222-2-2-222-22-20000-2-2220000000000000000200-20000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-2222-2-2000000000000000000000-2200000000000
χ2822222222-2-2-2-2-2-222222-2-2-2-22-2-2220000000000000000000002-200000000000
χ292-22-222-2-222-2-202002-20000-2000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i200000000000000002−22−200
χ302-22-222-2-222-2-202002-20000-2000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000000000000000−22−2200
χ312-22-222-2-222-2-202002-20000-200000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000000000000000−22−2200
χ322-22-222-2-222-2-202002-20000-200000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200000000000000002−22−200
χ332-22-222-2-2-2-2220200-220000-2000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i200000000000000002−2−2200
χ342-22-222-2-2-2-2220200-220000-2000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000000000−222−200
χ352-22-222-2-2-2-2220200-220000-200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000000000−222−200
χ362-22-222-2-2-2-2220200-220000-200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i200000000000000002−2−2200
χ372-2-2-2-22222-22-2000000-22-20022-22-200002−22−22−22−222−2−222−2−200000000000000
χ382-2-2-2-22222-22-2000000-22-20022-22-20000−22−22−22−22−2−222−2−22200000000000000
χ392-2-2-2-22222-22-2000000-22-2002-22-2200002−22−22−22−2−2−222−2−22200000000000000
χ402-2-2-2-22222-22-2000000-22-2002-22-220000−22−22−22−2222−2−222−2−200000000000000
χ412-2-2-2-2222-22-22000000-2-220022-2-2200002−22−2−22−2222−2−2−2−22200000000000000
χ422-2-2-2-2222-22-22000000-2-220022-2-220000−22−222−22−2−2−22222−2−200000000000000
χ432-2-2-2-2222-22-22000000-2-22002-222-200002−22−2−22−22−2−22222−2−200000000000000
χ442-2-2-2-2222-22-22000000-2-22002-222-20000−22−222−22−222−2−2−2−22200000000000000
χ45444-4-4-44-40000004i−4i0000000000000000000000002-22-22i−2i2i−2i00000000000000
χ46444-4-4-44-40000004i−4i000000000000000000000000-22-22−2i2i−2i2i00000000000000
χ47444-4-4-44-4000000−4i4i0000000000000000000000002-22-2−2i2i−2i2i00000000000000
χ48444-4-4-44-4000000−4i4i000000000000000000000000-22-222i−2i2i−2i00000000000000
χ4944-44-44-4-44-4-44000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ5044-44-44-4-44-4-4400000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ5144-44-44-4-4-444-4000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ5244-44-44-4-4-444-400000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ534-44-444-4-444-4-40-400-4400004000000000000000000000000000000000000000
χ544-44-444-4-4-4-4440-4004-400004000000000000000000000000000000000000000
χ554-4-444-44-40000400000000-400000000000000000000002i2−2i2−2i22i200000000000000
χ564-4-444-44-40000400000000-40000000000000000000000−2i22i22i2−2i200000000000000
χ574-4-444-44-40000-400000000400000000000000000022−22−2222000000000000000000
χ584-4-444-44-40000-4000000004000000000000000000−222222−22000000000000000000
χ594-4-4-4-44444-44-40000004-4400-400000000000000000000000000000000000000
χ604-4-4-4-4444-44-4400000044-400-400000000000000000000000000000000000000
χ6188-8-88-8-88000000000000000000000000000000000000000000000000000000
χ628-888-8-8-88000000000000000000000000000000000000000000000000000000

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