Finite Group Databasebeta

← Group #170306

Character table — Group #170306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-11-1-11-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-11-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-111-111111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1111-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-1-1-111-1-111-11
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111111-11-1-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-11
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-11-1-1111-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1111-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1111-1-111-1-1-11
χ1722222222222222-2-2-2-222-2-2-2-200000000000000000000000000202-20-2000000
χ1822222222222222-2-2-2-222-2-2-2-200000000000000000000000000-20-2202000000
χ19222222222222-2-222-2-2-2-222-2-2222200000000000000000000000-200-20000000
χ20222222222222-2-222-2-2-2-222-2-2-2-2-2-20000000000000000000000020020000000
χ21222222222222-2-2-2-222-2-2-2-222000022220000000000000000-2-2000000000000
χ22222222222222-2-2-2-222-2-2-2-2220000-2-2-2-2000000000000000022000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-222000022-2-200000000000000002-2000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2220000-2-2220000000000000000-22000000000000
χ2522222222-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000200-20000000
χ2622222222-2-2-2-222-2-222-2-222-2-2-2-22200000000000000000000000-20020000000
χ2722222222-2-2-2-2-2-2222222-2-2-2-20000000000000000000000000020-220-2000000
χ2822222222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000-202-202000000
χ292-2-222-2-222i2i−2i−2i002i−2i00002-2002i−2i2-2000022−2−2i2i2−i2−i2i2i2−i2−i222−2−200000000000000
χ302-2-222-2-222i2i−2i−2i002i−2i00002-2002i−2i2-20000−2−222−i2−i2i2i2−i2−i2i2i2−2−22200000000000000
χ312-2-222-2-222i2i−2i−2i002i−2i00002-200−2i2i-22000022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000000000
χ322-2-222-2-222i2i−2i−2i002i−2i00002-200−2i2i-220000−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000000000
χ332-2-222-2-22−2i−2i2i2i00−2i2i00002-2002i−2i-22000022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000000000
χ342-2-222-2-22−2i−2i2i2i00−2i2i00002-2002i−2i-220000−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000000000
χ352-2-222-2-22−2i−2i2i2i00−2i2i00002-200−2i2i2-2000022−2−2−i2−i2i2i2−i2−i2i2i222−2−200000000000000
χ362-2-222-2-22−2i−2i2i2i00−2i2i00002-200−2i2i2-20000−2−222i2i2−i2−i2i2i2−i2−i2−2−22200000000000000
χ372-2-22-222-22i−2i2i−2i00002i−2i00002-200002i−2i2-22−22−2i2−i2i2−i20000000000000000i2−i22−200
χ382-2-22-222-22i−2i2i−2i00002i−2i00002-200002i−2i2-2−22−22−i2i2−i2i20000000000000000−i2i2−2200
χ392-2-22-222-22i−2i2i−2i00002i−2i00002-20000−2i2i-222−22−2i2−i2i2−i20000000000000000−i2i2−2200
χ402-2-22-222-22i−2i2i−2i00002i−2i00002-20000−2i2i-22−22−22−i2i2−i2i20000000000000000i2−i22−200
χ412-2-22-222-2−2i2i−2i2i0000−2i2i00002-200002i−2i-222−22−2−i2i2−i2i20000000000000000i2−i2−2200
χ422-2-22-222-2−2i2i−2i2i0000−2i2i00002-200002i−2i-22−22−22i2−i2i2−i20000000000000000−i2i22−200
χ432-2-22-222-2−2i2i−2i2i0000−2i2i00002-20000−2i2i2-22−22−2−i2i2−i2i20000000000000000−i2i22−200
χ442-2-22-222-2−2i2i−2i2i0000−2i2i00002-20000−2i2i2-2−22−22i2−i2i2−i20000000000000000i2−i2−2200
χ454444-4-4-4-44-4-44000000000000000000002-2-222-2-220000000000000000000000
χ464444-4-4-4-44-4-4400000000000000000000-222-2-222-20000000000000000000000
χ474444-4-4-4-4-444-4000000000000000000002-2-22-222-20000000000000000000000
χ484444-4-4-4-4-444-400000000000000000000-222-22-2-220000000000000000000000
χ4944-4-4-44-4400004i−4i000000000000000000000000002-22-22i−2i2i−2i00000000000000
χ5044-4-4-44-4400004i−4i00000000000000000000000000-22-22−2i2i−2i2i00000000000000
χ5144-4-4-44-440000−4i4i000000000000000000000000002-22-2−2i2i−2i2i00000000000000
χ5244-4-4-44-440000−4i4i00000000000000000000000000-22-222i−2i2i−2i00000000000000
χ534-44-4-4-44400000000004-40000000000000000000000002i2−2i2−2i22i200000000000000
χ544-44-4-4-44400000000004-4000000000000000000000000−2i22i22i2−2i200000000000000
χ554-44-4-4-4440000000000-44000000000000000000002i2−2i2−2i22i2000000000000000000
χ564-44-4-4-4440000000000-4400000000000000000000−2i22i22i2−2i2000000000000000000
χ574-4-444-4-444i4i−4i−4i00−4i4i0000-440000000000000000000000000000000000000000
χ584-4-444-4-44−4i−4i4i4i004i−4i0000-440000000000000000000000000000000000000000
χ594-4-44-444-44i−4i4i−4i0000−4i4i0000-4400000000000000000000000000000000000000
χ604-4-44-444-4−4i4i−4i4i00004i−4i0000-4400000000000000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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