Finite Group Databasebeta

← Group #170101

Character table — Group #170101

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1
χ911111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-11-111-1-11-1
χ1011111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-11-1-1-111-11
χ1111111111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-11-1-111-11
χ1211111111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1111-1-11-1
χ1311111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1111-111-1-1-11
χ1411111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-1111-1
χ1511111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-1-1-11-1-1111-1
χ1611111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-1111-1-1-11
χ1722222222222222-2-2-2-2-2-222-2-2000000000000000000000000002-22-200000000
χ1822222222222222-2-2-2-2-2-222-2-200000000000000000000000000-22-2200000000
χ19222222222222-2-22-2-2-222-2-22-2002222000000000000000000000000-2-2000000
χ20222222222222-2-22-2-2-222-2-22-200-2-2-2-200000000000000000000000022000000
χ21222222222222-2-2-2222-2-2-2-2-22220000220000000000000000-2-2000000000000
χ22222222222222-2-2-2222-2-2-2-2-22-2-20000-2-2000000000000000022000000000000
χ2322222222-2-2-2-2222-222-2-2-2-22-20022-2-2000000000000000000000000-22000000
χ2422222222-2-2-2-2222-222-2-2-2-22-200-2-2220000000000000000000000002-2000000
χ2522222222-2-2-2-222-22-2-222-2-2-22220000-2-200000000000000002-2000000000000
χ2622222222-2-2-2-222-22-2-222-2-2-22-2-20000220000000000000000-22000000000000
χ2722222222-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000-222-200000000
χ292-222-2-2-2222-2-20020002-200-20002i−2i2i−2i00i2i2−i2−i2i2i2−i2−i200000000000000002−22−200
χ302-222-2-2-2222-2-20020002-200-20002i−2i2i−2i00−i2−i2i2i2−i2−i2i2i20000000000000000−22−2200
χ312-222-2-2-2222-2-20020002-200-2000−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i20000000000000000−22−2200
χ322-222-2-2-2222-2-20020002-200-2000−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i200000000000000002−22−200
χ332-222-2-2-22-2-222002000-2200-20002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i200000000000000002−2−2200
χ342-222-2-2-22-2-222002000-2200-20002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i20000000000000000−222−200
χ352-222-2-2-22-2-222002000-2200-2000−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i20000000000000000−222−200
χ362-222-2-2-22-2-222002000-2200-2000−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i200000000000000002−2−2200
χ372-22-222-2-22-22-2000-22-20000022i−2i00002i−2ii2−i2i2−i2i2−i2i2−i222−2−222−2−200000000000000
χ382-22-222-2-22-22-2000-22-20000022i−2i00002i−2i−i2i2−i2i2−i2i2−i2i2−2−222−2−22200000000000000
χ392-22-222-2-22-22-2000-22-2000002−2i2i0000−2i2ii2−i2i2−i2i2−i2i2−i2−2−222−2−22200000000000000
χ402-22-222-2-22-22-2000-22-2000002−2i2i0000−2i2i−i2i2−i2i2−i2i2−i2i222−2−222−2−200000000000000
χ412-22-222-2-2-22-22000-2-220000022i−2i0000−2i2ii2−i2i2−i2−i2i2−i2i222−2−2−2−22200000000000000
χ422-22-222-2-2-22-22000-2-220000022i−2i0000−2i2i−i2i2−i2i2i2−i2i2−i2−2−22222−2−200000000000000
χ432-22-222-2-2-22-22000-2-22000002−2i2i00002i−2ii2−i2i2−i2−i2i2−i2i2−2−22222−2−200000000000000
χ442-22-222-2-2-22-22000-2-22000002−2i2i00002i−2i−i2i2−i2i2i2−i2i2−i222−2−2−2−22200000000000000
χ45444-4-4-44-44-4-44000000000000000000002-2-222-2-220000000000000000000000
χ46444-4-4-44-44-4-4400000000000000000000-222-2-222-20000000000000000000000
χ47444-4-4-44-4-444-4000000000000000000002-2-22-222-20000000000000000000000
χ48444-4-4-44-4-444-400000000000000000000-222-22-2-220000000000000000000000
χ4944-444-4-4-400004-4000000000000000000000000002-22-22-22-200000000000000
χ5044-444-4-4-400004-400000000000000000000000000-22-22-22-2200000000000000
χ5144-444-4-4-40000-44000000000000000000000000002-22-2-22-2200000000000000
χ5244-444-4-4-40000-4400000000000000000000000000-22-222-22-200000000000000
χ534-444-4-4-4444-4-400-4000-44004000000000000000000000000000000000000000
χ544-444-4-4-44-4-44400-40004-4004000000000000000000000000000000000000000
χ554-44-444-4-44-44-40004-4400000-400000000000000000000000000000000000000
χ564-44-444-4-4-44-4400044-400000-400000000000000000000000000000000000000
χ574-4-4-44-4440000000000004-4000000000000000000000022−22−222200000000000000
χ584-4-4-44-4440000000000004-40000000000000000000000−222222−2200000000000000
χ594-4-4-44-444000000000000-4400000000000000000022−22−2222000000000000000000
χ604-4-4-44-444000000000000-44000000000000000000−222222−22000000000000000000
χ6188-8-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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