Finite Group Databasebeta

← Group #299581

Character table — Group #299581

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order12222244444488884444444888888448888888888888888888822444444444424
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11-11-11-11111-1-1
χ611111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-11-11-1-1-1-111
χ711111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-11-11-11-1-1-1-1-111
χ811111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-11-111111-1-1
χ9111111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-11
χ10111111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-1
χ11111111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111-1
χ12111111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-11
χ13111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-111-1-1111-1-11-1
χ14111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-1-111-1-1-111-11
χ15111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-111-1-11-1-111-11
χ16111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111-111-1-11-1
χ172222222-2-2-2-222222222-2-2-2-222-2-2-2-22-20000000022-2-20000000000000000000000
χ182222222-2-2-2-2222222-2-222-2-222-2-2-2-2-2200000000-2-2220000000000000000000000
χ192222222-2-2-2-22-2-2-2-2222-2-2-2-2-2-222222-200000000-2-2220000000000000000000000
χ202222222-2-2-2-22-2-2-2-22-2-222-2-2-2-22222-220000000022-2-20000000000000000000000
χ21222222-22222-20000-22222-2-2000000-2-222-2-222-2-200000000000000000000000000
χ22222222-22222-20000-22222-2-2000000-2-2-2-222-2-22200000000000000000000000000
χ23222222-22222-20000-2-2-2-2-2-2-20000002222-2-2-2-22200000000000000000000000000
χ24222222-22222-20000-2-2-2-2-2-2-200000022-2-22222-2-200000000000000000000000000
χ25222222-2-2-2-2-2-20000-222-2-222000000-2200000000000022-2-222-2-200000000000000
χ26222222-2-2-2-2-2-20000-222-2-222000000-22000000000000-2-222-2-22200000000000000
χ27222222-2-2-2-2-2-20000-2-2-222220000002-200000000000022-2-2-2-22200000000000000
χ28222222-2-2-2-2-2-20000-2-2-222220000002-2000000000000-2-22222-2-200000000000000
χ292222-2-2222-2-222222-200002-2-2-222-2-20000000000000000000000020-20-202000000
χ302222-2-2222-2-222222-200002-2-2-222-2-200000000000000000000000-202020-2000000
χ312222-2-2222-2-22-2-2-2-2-200002-222-2-222000000000000000000000002020-20-2000000
χ322222-2-2222-2-22-2-2-2-2-200002-222-2-22200000000000000000000000-20-20202000000
χ332222-2-22-2-22222222-20000-22-2-2-2-222000000000000000000000020-20-2020000000
χ342222-2-22-2-22222222-20000-22-2-2-2-2220000000000000000000000-202020-20000000
χ352222-2-22-2-2222-2-2-2-2-20000-222222-2-200000000000000000000002020-20-20000000
χ362222-2-22-2-2222-2-2-2-2-20000-222222-2-20000000000000000000000-20-202020000000
χ372-22-22-202-22-20i2i2−i2−i202-22-200i2−i2i2−i2i2−i200002i−2i002i−2ii2−i2i2−i22−22−22−22−200000000000000
χ382-22-22-202-22-20i2i2−i2−i202-22-200i2−i2i2−i2i2−i20000−2i2i00−2i2ii2−i2i2−i2−22−22−22−2200000000000000
χ392-22-22-202-22-20i2i2−i2−i20-22-2200i2−i2i2−i2i2−i200002i−2i00−2i2i−i2i2−i2i22−22−2−22−2200000000000000
χ402-22-22-202-22-20i2i2−i2−i20-22-2200i2−i2i2−i2i2−i20000−2i2i002i−2i−i2i2−i2i2−22−222−22−200000000000000
χ412-22-22-202-22-20−i2−i2i2i202-22-200−i2i2−i2i2−i2i200002i−2i002i−2i−i2i2−i2i2−22−22−22−2200000000000000
χ422-22-22-202-22-20−i2−i2i2i202-22-200−i2i2−i2i2−i2i20000−2i2i00−2i2i−i2i2−i2i22−22−22−22−200000000000000
χ432-22-22-202-22-20−i2−i2i2i20-22-2200−i2i2−i2i2−i2i200002i−2i00−2i2ii2−i2i2−i2−22−222−22−200000000000000
χ442-22-22-202-22-20−i2−i2i2i20-22-2200−i2i2−i2i2−i2i20000−2i2i002i−2ii2−i2i2−i22−22−2−22−2200000000000000
χ452-22-22-20-22-220i2i2−i2−i202-2-2200i2−i2−i2i2−i2i2002i−2i002i−2i00i2−i2−i2i22−2−222−2−2200000000000000
χ462-22-22-20-22-220i2i2−i2−i202-2-2200i2−i2−i2i2−i2i200−2i2i00−2i2i00i2−i2−i2i2−222−2−222−200000000000000
χ472-22-22-20-22-220i2i2−i2−i20-222-200i2−i2−i2i2−i2i2002i−2i00−2i2i00−i2i2i2−i22−2−22−222−200000000000000
χ482-22-22-20-22-220i2i2−i2−i20-222-200i2−i2−i2i2−i2i200−2i2i002i−2i00−i2i2i2−i2−222−22−2−2200000000000000
χ492-22-22-20-22-220−i2−i2i2i202-2-2200−i2i2i2−i2i2−i2002i−2i002i−2i00−i2i2i2−i2−222−2−222−200000000000000
χ502-22-22-20-22-220−i2−i2i2i202-2-2200−i2i2i2−i2i2−i200−2i2i00−2i2i00−i2i2i2−i22−2−222−2−2200000000000000
χ512-22-22-20-22-220−i2−i2i2i20-222-200−i2i2i2−i2i2−i2002i−2i00−2i2i00i2−i2−i2i2−222−22−2−2200000000000000
χ522-22-22-20-22-220−i2−i2i2i20-222-200−i2i2i2−i2i2−i200−2i2i002i−2i00i2−i2−i2i22−2−22−222−200000000000000
χ534444-4-4-444-4-4-4000040000-44000000000000000000000000000000000000000000
χ544444-4-4-4-4-444-40000400004-4000000000000000000000000000000000000000000
χ5544-4-400-4000044i−4i4i−4i00000000000000000000000000000000000000000002-22i−2i00
χ5644-4-400-4000044i−4i4i−4i0000000000000000000000000000000000000000000-22−2i2i00
χ5744-4-400-400004−4i4i−4i4i00000000000000000000000000000000000000000002-2−2i2i00
χ5844-4-400-400004−4i4i−4i4i0000000000000000000000000000000000000000000-222i−2i00
χ594-44-4-4404-4-4402i22i2−2i2−2i20000000−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ604-44-4-4404-4-440−2i2−2i22i22i200000002i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ614-44-4-440-444-402i22i2−2i2−2i20000000−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ624-44-4-440-444-40−2i2−2i22i22i200000002i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ6388-8-80080000-800000000000000000000000000000000000000000000000000000
χ648-8-880000000042−42−42420000000000000000000000000000000000000000000000000
χ658-8-8800000000−424242−420000000000000000000000000000000000000000000000000

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