Finite Group Databasebeta

← Group #138656

Character table — Group #138656

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222224444888844448816161616161616162244888888161616161616161616161616888888882488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-111-1-1-1-1-11-11-111iiii−i−i−i−i1-11-11-111-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-111-1-1-1-1-11-11-111iiii−i−i−i−i1-11-11-111-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1-111-1-1-1-1-11-11-111iiii−i−i−i−i-11-111-1-1-111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1-111-1-1-1-1-11-11-111iiii−i−i−i−i-11-111-1-1-111ii−i−i−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1-111-1-1-1-1-11-11-111−i−i−i−iiiii1-11-11-111-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1-111-1-1-1-1-11-11-111−i−i−i−iiiii1-11-11-111-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1-111-1-1-1-1-11-11-111−i−i−i−iiiii-11-111-1-1-111−i−iiiiiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1-111-1-1-1-1-11-11-111−i−i−i−iiiii-11-111-1-1-111−i−iiiiiii−i−i−i−i-1-111ii−i−i1-1−ii
χ1722222222222222-2-2-2-222222222220000-2-20000-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-20000-2-20000222200000000000000000000
χ192222222222-2-2-2-22222-2-2000000002222-2-2-2-2-2-2000000000000000000000000
χ202222222222-2-2-2-22222-2-200000000-2-2-2-2-2-22222000000000000000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-200000000000022000000002i2i−2i−2i2i2i−2i−2i000000000000
χ222222222222-2-2-2-2-2-2-2-2-2-20000000000002200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ23222222-2-2-2-200002-2-2200i2i2−i2−i2i2i2−i2−i20000002i−2i2i−2ii2−i2i2−i22−22−22−22−2000000000000
χ24222222-2-2-2-200002-2-2200i2i2−i2−i2i2i2−i2−i2000000−2i2i−2i2ii2−i2i2−i2−22−22−22−22000000000000
χ25222222-2-2-2-200002-2-2200−i2−i2i2i2−i2−i2i2i20000002i−2i2i−2i−i2i2−i2i2−22−22−22−22000000000000
χ26222222-2-2-2-200002-2-2200−i2−i2i2i2−i2−i2i2i2000000−2i2i−2i2i−i2i2−i2i22−22−22−22−2000000000000
χ27222222-2-2-2-20000-222-200i2i2−i2−i2i2i2−i2−i22-2-22000000−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ28222222-2-2-2-20000-222-200i2i2−i2−i2i2i2−i2−i2-222-2000000−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ29222222-2-2-2-20000-222-200−i2−i2i2i2−i2−i2i2i22-2-22000000i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ30222222-2-2-2-20000-222-200−i2−i2i2i2−i2−i2i2i2-222-2000000i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ312222-2-22-2-22000022-2-20022−2−2−2−2220000002i−2i−2i2i2−2−22−i2i2−i2i2i2−i2i2−i2000000000000
χ322222-2-22-2-22000022-2-20022−2−2−2−222000000−2i2i2i−2i2−2−22i2−i2i2−i2−i2i2−i2i2000000000000
χ332222-2-22-2-22000022-2-200−2−22222−2−20000002i−2i−2i2i−222−2i2−i2i2−i2−i2i2−i2i2000000000000
χ342222-2-22-2-22000022-2-200−2−22222−2−2000000−2i2i2i−2i−222−2−i2i2−i2i2i2−i2i2−i2000000000000
χ352222-2-22-2-220000-2-2220022−2−2−2−22222-2-2000000−222−22−2−22−222−2000000000000
χ362222-2-22-2-220000-2-2220022−2−2−2−222-2-222000000−222−2−222−22−2−22000000000000
χ372222-2-22-2-220000-2-22200−2−22222−2−222-2-20000002−2−22−222−22−2−22000000000000
χ382222-2-22-2-220000-2-22200−2−22222−2−2-2-2220000002−2−222−2−22−222−2000000000000
χ392222-2-2-222-222222-22-2-2-2000000002-22-2-22-2-222000000000000000000000000
χ402222-2-2-222-222222-22-2-2-200000000-22-22-2222-2-2000000000000000000000000
χ412222-2-2-222-22222-22-22-2-20000000000002-20000000022-2-2-2-222000000000000
χ422222-2-2-222-22222-22-22-2-20000000000002-200000000-2-22222-2-2000000000000
χ432222-2-2-222-2-2-2-2-2-22-22222i2i2i2i−2i−2i−2i−2i0000-220000−2i−2i2i2i00000000000000000000
χ442222-2-2-222-2-2-2-2-2-22-2222−2i−2i−2i−2i2i2i2i2i0000-2200002i2i−2i−2i00000000000000000000
χ452-2-222-22-22-222-2-200002-22i−2i2i−2i2i−2i2i−2i00000000000000000000002−22−2i2−i2i2−i20000
χ462-2-222-22-22-222-2-200002-22i−2i2i−2i2i−2i2i−2i0000000000000000000000−22−22−i2i2−i2i20000
χ472-2-222-22-22-222-2-200002-2−2i2i−2i2i−2i2i−2i2i00000000000000000000002−22−2−i2i2−i2i20000
χ482-2-222-22-22-222-2-200002-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000−22−22i2−i2i2−i20000
χ492-2-22-22-2-222-2-22200002-22-22-2-22-2200000000000000000000002−2−222−2−220000
χ502-2-22-22-2-222-2-22200002-22-22-2-22-220000000000000000000000−222−2−222−20000
χ512-2-22-22-2-222-2-22200002-2-22-222-22-200000000000000000000002−2−22−222−20000
χ522-2-22-22-2-222-2-22200002-2-22-222-22-20000000000000000000000−222−22−2−220000
χ534-4-444-44-44-4-4-4440000-44000000000000000000000000000000000000000000
χ544-4-444-4-44-44000000000022−22−222222−22−22220000000000000000000000000000000000
χ554-4-444-4-44-440000000000−222222−22−222222−220000000000000000000000000000000000
χ564-4-44-4444-4-400000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ574-4-44-4444-4-40000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ584-4-44-44-4-44444-4-40000-44000000000000000000000000000000000000000000
χ5988-8-80000004i2−4i24i2−4i2000000000000000000000000000000000000000000000000
χ6088-8-8000000−4i24i2−4i24i2000000000000000000000000000000000000000000000000
χ618-88-80000004i2−4i2−4i24i2000000000000000000000000000000000000000000000000
χ628-88-8000000−4i24i24i2−4i2000000000000000000000000000000000000000000000000

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