Finite Group Databasebeta

← Group #352341

Character table — Group #352341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222244444444444444444444448888888888888888883232323232323232
order12222244444444224444444488888888888888888888888888888824448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-11-1-111-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-111-1-11
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-11-11-1
χ911111111111111-1-11-1-11-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1
χ1011111111111111-1-11-1-11-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ1111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-111
χ1211111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-11111-1-1
χ1311111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-11-11-1-11
χ1411111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-11-111-1
χ1511111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-11-1-111-11-1
χ1611111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-111-1-11-11
χ1722222222-2-2-2-2-2-200200-2000022-2-2000000002-20000002i2i−2i−2i002i2i−2i−2i00000000
χ1822222222-2-2-2-2-2-200200-2000022-2-2000000002-2000000−2i−2i2i2i00−2i−2i2i2i00000000
χ1922222222-2-2-2-2-2-200200-20000-2-22200000000-220000002i2i−2i−2i00−2i−2i2i2i00000000
χ2022222222-2-2-2-2-2-200200-20000-2-22200000000-22000000−2i−2i2i2i002i2i−2i−2i00000000
χ21222222-2-222-2-2-2-200-200200000000000022-2-2002i2i−2i−2i002i−2i2i−2i2-2000000000000
χ22222222-2-222-2-2-2-200-200200000000000022-2-200−2i−2i2i2i00−2i2i−2i2i2-2000000000000
χ23222222-2-222-2-2-2-200-2002000000000000-2-222002i2i−2i−2i00−2i2i−2i2i-22000000000000
χ24222222-2-222-2-2-2-200-2002000000000000-2-22200−2i−2i2i2i002i−2i2i−2i-22000000000000
χ25222222-2-2-2-2222222-2-2-2-2-2-222000022-2-200000000002-22-2-2200000000000000
χ26222222-2-2-2-2222222-2-2-2-2-2-2220000-2-2220000000000-22-222-200000000000000
χ27222222-2-2-2-22222-2-2-222-222-2-2000022-2-200000000002-2-222-200000000000000
χ28222222-2-2-2-22222-2-2-222-222-2-20000-2-2220000000000-222-2-2200000000000000
χ292222-2-2222222-2-200-200-20000222222222222-2-20000-2-20000-2-2000000000000
χ302222-2-2222222-2-200-200-200002222-2-2-2-2-2-2-2-2-2-2000022000022000000000000
χ312222-2-2222222-2-200-200-20000-2-2-2-22222-2-2-2-2220000-2-2000022000000000000
χ322222-2-2222222-2-200-200-20000-2-2-2-2-2-2-2-22222220000220000-2-2000000000000
χ332222-2-222-2-2-2-22222-2222-2-2-2-222-2-200000000-222-22-200000000000000000000
χ342222-2-222-2-2-2-22222-2222-2-2-2-2-2-222000000002-2-22-2200000000000000000000
χ352222-2-222-2-2-2-222-2-2-2-2-22222222-2-200000000-22-22-2200000000000000000000
χ362222-2-222-2-2-2-222-2-2-2-2-222222-2-222000000002-22-22-200000000000000000000
χ372222-2-2-2-222-2-222222-2-2-222-2-20000000022-2-2000000000000-222-22-200000000
χ382222-2-2-2-222-2-222222-2-2-222-2-200000000-2-2220000000000002-2-22-2200000000
χ392222-2-2-2-222-2-222-2-2222-2-2-2220000000022-2-2000000000000-22-22-2200000000
χ402222-2-2-2-222-2-222-2-2222-2-2-22200000000-2-2220000000000002-22-22-200000000
χ412222-2-2-2-2-2-222-2-20020020000000022-2-20000002i−2i−2i2i-22000000−2i2i2i−2i00000000
χ422222-2-2-2-2-2-222-2-20020020000000022-2-2000000−2i2i2i−2i-220000002i−2i−2i2i00000000
χ432222-2-2-2-2-2-222-2-200200200000000-2-2220000002i−2i−2i2i2-20000002i−2i−2i2i00000000
χ442222-2-2-2-2-2-222-2-200200200000000-2-222000000−2i2i2i−2i2-2000000−2i2i2i−2i00000000
χ454-44-400004-40000000000000022−2222−222i2−2i22i2−2i2004i−4i00000000000000000000000000
χ464-44-400004-40000000000000022−2222−22−2i22i2−2i22i200−4i4i00000000000000000000000000
χ474-44-400004-400000000000000−2222−22222i2−2i22i2−2i200−4i4i00000000000000000000000000
χ484-44-400004-400000000000000−2222−2222−2i22i2−2i22i2004i−4i00000000000000000000000000
χ494-44-40000-440000000000000022−22−22222i2−2i2−2i22i24i−4i0000000000000000000000000000
χ504-44-40000-440000000000000022−22−2222−2i22i22i2−2i2−4i4i0000000000000000000000000000
χ514-44-40000-4400000000000000−222222−222i2−2i2−2i22i2−4i4i0000000000000000000000000000
χ524-44-40000-4400000000000000−222222−22−2i22i22i2−2i24i−4i0000000000000000000000000000
χ534-4-444-400004-44-40004i−4i04i−4i0000000000000000000000000000000000000000
χ544-4-444-400004-44-4000−4i4i0−4i4i0000000000000000000000000000000000000000
χ554-4-444-40000-44-444-40000004-400000000000000000000000000000000000000
χ564-4-444-40000-44-44-44000000-4400000000000000000000000000000000000000
χ574-4-44-4400004-4-444-4000000-4400000000000000000000000000000000000000
χ584-4-44-4400004-4-44-440000004-400000000000000000000000000000000000000
χ594-4-44-440000-444-40004i−4i0−4i4i0000000000000000000000000000000000000000
χ604-4-44-440000-444-4000−4i4i04i−4i0000000000000000000000000000000000000000
χ6188-8-8008-8000000000000000000000000000000000000000000000000000000
χ6288-8-800-88000000000000000000000000000000000000000000000000000000

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