Finite Group Databasebeta

← Group #242048

Character table — Group #242048

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444444444888888888888888822224444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11-1-11-11-1-11-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111-11-111-11-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-11-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-11111-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-11-1-1-1-1-11-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-1111-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-11-1-11111-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11-111111-1-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-11-111-1-11-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1111111111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11-1111-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-11-1-111-11-1-1-1-111
χ172222222222-2-222-2-22222-2-2-2-2-2-20000000000000000000002-2020000-2000000
χ182222222222-2-222-2-22222-2-2-2-2-2-2000000000000000000000-220-200002000000
χ192222222222-2-222-2-2-2-2-2-22222-2-2000000000000000000000220-20000-2000000
χ202222222222-2-222-2-2-2-2-2-22222-2-2000000000000000000000-2-20200002000000
χ2122222222-2-222-2-22222-2-222-2-2-2-200000000000000000000200-20-20020000000
χ2222222222-2-222-2-22222-2-222-2-2-2-200000000000000000000-20020200-20000000
χ2322222222-2-222-2-222-2-222-2-222-2-200000000000000000000200-20200-20000000
χ2422222222-2-222-2-222-2-222-2-222-2-200000000000000000000-20020-20020000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000002-200000000002-20000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000-220000000000-220000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000002-20000000000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-222000000000000000000-2200000000002-20000
χ292-222-22-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000002-22i−2i
χ302-222-22-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i2-200000000000000000000000000000000-22−2i2i
χ312-222-22-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000000002-2−2i2i
χ322-222-22-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-200000000000000000000000000000000-222i−2i
χ332-222-22-2-22-2-222-2-222i−2i2i−2i−2i2i−2i2i-220000000022-2-22i2i−2i−2i00000000000000000000
χ342-222-22-2-22-2-222-2-222i−2i2i−2i−2i2i−2i2i-2200000000-2-222−2i−2i2i2i00000000000000000000
χ352-222-22-2-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i-220000000022-2-2−2i−2i2i2i00000000000000000000
χ362-222-22-2-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i-2200000000-2-2222i2i−2i−2i00000000000000000000
χ372-222-22-2-2-222-2-222-22i−2i−2i2i2i−2i−2i2i-2200000000000000002-2000000002i−2i00000000
χ382-222-22-2-2-222-2-222-22i−2i−2i2i2i−2i−2i2i-220000000000000000-2200000000−2i2i00000000
χ392-222-22-2-2-222-2-222-2−2i2i2i−2i−2i2i2i−2i-2200000000000000002-200000000−2i2i00000000
χ402-222-22-2-2-222-2-222-2−2i2i2i−2i−2i2i2i−2i-220000000000000000-22000000002i−2i00000000
χ412-222-22-2-2-22-22-22-222i−2i−2i2i−2i2i2i−2i2-22i2i−2i−2i22-2-20000000000000000000000000000
χ422-222-22-2-2-22-22-22-222i−2i−2i2i−2i2i2i−2i2-2−2i−2i2i2i-2-2220000000000000000000000000000
χ432-222-22-2-2-22-22-22-22−2i2i2i−2i2i−2i−2i2i2-22i2i−2i−2i-2-2220000000000000000000000000000
χ442-222-22-2-2-22-22-22-22−2i2i2i−2i2i−2i−2i2i2-2−2i−2i2i2i22-2-20000000000000000000000000000
χ45444-44-4-4-44400-4-40000000000000000000022−2222−22000000000000000000000000
χ46444-44-4-4-44400-4-400000000000000000000−2222−2222000000000000000000000000
χ47444-44-4-4-4-4-400440000000000000000000000002i2−2i22i2−2i200000000000000000000
χ48444-44-4-4-4-4-40044000000000000000000000000−2i22i2−2i22i200000000000000000000
χ4944-44-4-44-4004-400-4400000000002i2−2i22i2−2i200000000000000000000000000000000
χ5044-44-4-44-4004-400-440000000000−2i22i2−2i22i200000000000000000000000000000000
χ5144-44-4-44-400-44004-4000000000000002i2−2i22i2−2i20000000000000000000000000000
χ5244-44-4-44-400-44004-400000000000000−2i22i2−2i22i20000000000000000000000000000
χ534-44-4-4-4444-400-440000000000000000000022−22−2222000000000000000000000000
χ544-44-4-4-4444-400-4400000000000000000000−222222−22000000000000000000000000
χ554-44-4-4-444-44004-400000000000000000000000022−22−222200000000000000000000
χ564-44-4-4-444-44004-4000000000000000000000000−222222−2200000000000000000000
χ574-4-444-4-44004400-4-4000000000000002i2−2i2−2i22i20000000000000000000000000000
χ584-4-444-4-44004400-4-400000000000000−2i22i22i2−2i20000000000000000000000000000
χ594-4-444-4-4400-4-40044000000000022−22−222200000000000000000000000000000000
χ604-4-444-4-4400-4-400440000000000−222222−2200000000000000000000000000000000
χ6188-8-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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