Finite Group Databasebeta

← Group #170237

Character table — Group #170237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444422444444444444444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-11-11-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-11-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-1-1-111
χ911111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1111-11-1-111-11
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1111-1111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-11-1-1111-1
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-1-11
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1-111-111-1-1-11
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111111111-1-1-1-11-11-1-111-1-1-1111-1
χ1722222222222222-2-2-2-22-2-2-2-22000000000000000000000000200200-2-2000000
χ1822222222222222-2-2-2-22-2-2-2-22000000000000000000000000-200-20022000000
χ19222222222222-2-222-2-2-2-2-222-222220000000000000000000000-20-2000000000
χ20222222222222-2-222-2-2-2-2-222-2-2-2-2-20000000000000000000000202000000000
χ21222222222222-2-2-2-222-222-2-2-20000222200000000000000000-2000-200000000
χ22222222222222-2-2-2-222-222-2-2-20000-2-2-2-2000000000000000002000200000000
χ2322222222-2-2-2-22222-2-2-222-2-2-2000022-2-200000000000000000-2000200000000
χ2422222222-2-2-2-22222-2-2-222-2-2-20000-2-222000000000000000002000-200000000
χ2522222222-2-2-2-222-2-222-2-2-222-222-2-2000000000000000000000020-2000000000
χ2622222222-2-2-2-222-2-222-2-2-222-2-2-2220000000000000000000000-202000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-22000000000000000000000000200-200-22000000
χ2822222222-2-2-2-2-2-222222-2-2-2-22000000000000000000000000-2002002-2000000
χ2922-2-2-222-22i2i−2i−2i002i−2i000002-202i−2i2-20000i2i2−i2−i222−2−222−2−2i2i2−i2−i200000000000000
χ3022-2-2-222-22i2i−2i−2i002i−2i000002-202i−2i2-20000−i2−i2i2i2−2−222−2−222−i2−i2i2i200000000000000
χ3122-2-2-222-22i2i−2i−2i002i−2i000002-20−2i2i-220000i2i2−i2−i222−2−2−2−222−i2−i2i2i200000000000000
χ3222-2-2-222-22i2i−2i−2i002i−2i000002-20−2i2i-220000−i2−i2i2i2−2−22222−2−2i2i2−i2−i200000000000000
χ3322-2-2-222-2−2i−2i2i2i00−2i2i000002-202i−2i-220000i2i2−i2−i2−2−22222−2−2−i2−i2i2i200000000000000
χ3422-2-2-222-2−2i−2i2i2i00−2i2i000002-202i−2i-220000−i2−i2i2i222−2−2−2−222i2i2−i2−i200000000000000
χ3522-2-2-222-2−2i−2i2i2i00−2i2i000002-20−2i2i2-20000i2i2−i2−i2−2−222−2−222i2i2−i2−i200000000000000
χ3622-2-2-222-2−2i−2i2i2i00−2i2i000002-20−2i2i2-20000−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000000000
χ372-222-2-22-22i−2i2i−2i00002i−2i02-200000002i−2i2-2000000002−22−2i2−i2i2−i200000000i2−i22−200
χ382-222-2-22-22i−2i2i−2i00002i−2i02-200000002i−2i2-200000000−22−22−i2i2−i2i200000000−i2i2−2200
χ392-222-2-22-22i−2i2i−2i00002i−2i02-20000000−2i2i-22000000002−22−2i2−i2i2−i200000000−i2i2−2200
χ402-222-2-22-22i−2i2i−2i00002i−2i02-20000000−2i2i-2200000000−22−22−i2i2−i2i200000000i2−i22−200
χ412-222-2-22-2−2i2i−2i2i0000−2i2i02-200000002i−2i-22000000002−22−2−i2i2−i2i200000000i2−i2−2200
χ422-222-2-22-2−2i2i−2i2i0000−2i2i02-200000002i−2i-2200000000−22−22i2−i2i2−i200000000−i2i22−200
χ432-222-2-22-2−2i2i−2i2i0000−2i2i02-20000000−2i2i2-2000000002−22−2−i2i2−i2i200000000−i2i22−200
χ442-222-2-22-2−2i2i−2i2i0000−2i2i02-20000000−2i2i2-200000000−22−22i2−i2i2−i200000000i2−i2−2200
χ45444-4-4-4-44000000000040000-400000000000022−2222−220000000000000000000000
χ46444-4-4-4-44000000000040000-4000000000000−2222−22220000000000000000000000
χ47444-4-4-4-440000000000-400004000000002i2−2i22i2−2i200000000000000000000000000
χ48444-4-4-4-440000000000-40000400000000−2i22i2−2i22i200000000000000000000000000
χ4944-444-4-4-400004-40000000000000000002-2-222-2-220000000000000000000000
χ5044-444-4-4-400004-4000000000000000000-222-2-222-20000000000000000000000
χ5144-444-4-4-40000-440000000000000000002-2-22-222-20000000000000000000000
χ5244-444-4-4-40000-44000000000000000000-222-22-2-220000000000000000000000
χ5344-4-4-444-44i4i−4i−4i00−4i4i00000-44000000000000000000000000000000000000000
χ5444-4-4-444-4−4i−4i4i4i004i−4i00000-44000000000000000000000000000000000000000
χ554-444-4-44-44i−4i4i−4i0000−4i4i0-4400000000000000000000000000000000000000000
χ564-444-4-44-4−4i4i−4i4i00004i−4i0-4400000000000000000000000000000000000000000
χ574-4-4-44-4444-4-4400000000000000000000000000002-2-222-2-2200000000000000
χ584-4-4-44-4444-4-440000000000000000000000000000-222-2-222-200000000000000
χ594-4-4-44-444-444-400000000000000000000000000002-2-22-222-200000000000000
χ604-4-4-44-444-444-40000000000000000000000000000-222-22-2-2200000000000000
χ618-88-888-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-88-88000000000000000000000000000000000000000000000000000000

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