Finite Group Databasebeta

← Group #239251

Character table — Group #239251

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444442244444444888888888888888822444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1
χ121111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111
χ131111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ172222222222-2-2-2-2222222-2-2-2-2-2-20000000022-2-222-2-200000000000000000000
χ182222222222-2-2-2-2222222-2-2-2-2-2-200000000-2-222-2-22200000000000000000000
χ192222222222-2-2-2-222-2-2-2-222-2-2220000000022-2-2-2-22200000000000000000000
χ202222222222-2-2-2-222-2-2-2-222-2-22200000000-2-22222-2-200000000000000000000
χ2122222222-2-22222-2-222-2-222-2-2-2-20000000000000000002-22-200000000000000
χ2222222222-2-22222-2-222-2-222-2-2-2-2000000000000000000-22-2200000000000000
χ2322222222-2-22222-2-2-2-222-2-2-2-2220000000000000000002-2-2200000000000000
χ2422222222-2-22222-2-2-2-222-2-2-2-222000000000000000000-222-200000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000002i−2i2i−2i
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000−2i2i−2i2i
χ2722222222-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000000000−2i2i2i−2i
χ292-2-22-2-2222222-2-2-2-22-22-22-22-22-200000000000000000000000000002i−2i2i−2i0000
χ302-2-22-2-2222222-2-2-2-22-22-22-22-22-20000000000000000000000000000−2i2i−2i2i0000
χ312-2-22-2-2222222-2-2-2-2-22-22-222-2-2200000000000000000000000000002i−2i−2i2i0000
χ322-2-22-2-2222222-2-2-2-2-22-22-222-2-220000000000000000000000000000−2i2i2i−2i0000
χ332-2-22-2-22222-2-222-2-22-22-2-22-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ342-2-22-2-22222-2-222-2-22-22-2-22-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ352-2-22-2-22222-2-222-2-2-22-222-2-222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ362-2-22-2-22222-2-222-2-2-22-222-2-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ372-2-22-2-222-2-222-2-2222-2-222-2-22-2200000000000000002-200002-2000000000000
χ382-2-22-2-222-2-222-2-2222-2-222-2-22-220000000000000000-220000-22000000000000
χ392-2-22-2-222-2-222-2-222-222-2-22-222-200000000000000002-20000-22000000000000
χ402-2-22-2-222-2-222-2-222-222-2-22-222-20000000000000000-2200002-2000000000000
χ412-2-22-2-222-2-2-2-222222-2-22-222-22-20000000000000000000000002-22-200000000
χ422-2-22-2-222-2-2-2-222222-2-22-222-22-2000000000000000000000000-22-2200000000
χ432-2-22-2-222-2-2-2-22222-222-22-22-2-220000000000000000000000002-2-2200000000
χ442-2-22-2-222-2-2-2-22222-222-22-22-2-22000000000000000000000000-222-200000000
χ454444-4-4-4-44-400004-40000000000000022−2222−220000000000000000000000000000
χ464444-4-4-4-44-400004-400000000000000−2222−22220000000000000000000000000000
χ474444-4-4-4-4-440000-44000000000022−2222−2200000000000000000000000000000000
χ484444-4-4-4-4-440000-440000000000−2222−222200000000000000000000000000000000
χ4944-4-44-44-4004-44-40000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5044-4-44-44-4004-44-4000000000000000000000000−2i22i2−2i22i200000000000000000000
χ5144-4-44-44-400-44-440000000000000000000000002i2−2i2−2i22i200000000000000000000
χ5244-4-44-44-400-44-44000000000000000000000000−2i22i22i2−2i200000000000000000000
χ534-44-4-444-4004-4-44000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ544-44-4-444-4004-4-4400000000000000000000−2i22i2−2i22i2000000000000000000000000
χ554-44-4-444-400-444-4000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ564-44-4-444-400-444-400000000000000000000−2i22i22i2−2i2000000000000000000000000
χ574-4-4444-4-44-40000-44000000000000002i2−2i2−2i22i20000000000000000000000000000
χ584-4-4444-4-44-40000-4400000000000000−2i22i22i2−2i20000000000000000000000000000
χ594-4-4444-4-4-4400004-400000000002i2−2i2−2i22i200000000000000000000000000000000
χ604-4-4444-4-4-4400004-40000000000−2i22i22i2−2i200000000000000000000000000000000
χ6188-8-8-88-88000000000000000000000000000000000000000000000000000000
χ628-88-88-8-88000000000000000000000000000000000000000000000000000000

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