Finite Group Databasebeta

← Group #316656

Character table — Group #316656

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888244444888888888822444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-1111111-11111-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-111-1-11111-1-1
χ9111111111111111111-1-1-1-11111-1-11111-1-1111111-1-111-111-1-1-1-1-111-1-1-1-1-1-111
χ10111111111111111111-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-1-111-111-1-111-1-111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-11-1-1-1-1111111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-11111111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-111-1-1-1111111-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-111-1-1-111-1-1-1-1111111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-1111-1-1-1-1-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111-1-11111111-1-1-1-1-1-1
χ17222222222-222-2-22-2-2-222222222-2-20000-2-20000-2-22200000000000000000000
χ18222222222-222-2-22-2-2-22222-2-2-2-2-2-2000022000022-2-200000000000000000000
χ19222222222-222-2-22-2-2-2-2-2-2-22222220000220000-2-2-2-200000000000000000000
χ20222222222-222-2-22-2-2-2-2-2-2-2-2-2-2-2220000-2-20000222200000000000000000000
χ2122222222-22-2-222-22-2-222-2-20000-2222-2-200000000000020000-2000000000000
χ2222222222-22-2-222-22-2-222-2-20000-22-2-222000000000000-200002000000000000
χ2322222222-22-2-222-22-2-2-2-22200002-222-2-2000000000000-200002000000000000
χ2422222222-22-2-222-22-2-2-2-22200002-2-2-22200000000000020000-2000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200002-20000002i2i−2i−2i0000000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-200002-2000000−2i−2i2i2i000000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-2220000-220000002i2i−2i−2i000000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-2220000-22000000−2i−2i2i2i0000000000000000002i−2i0000
χ292-222-2-22-220-2-20020002i−2i2i−2i2i2i−2i−2i000000000000002-200000000002−22−200i2−i2i2−i2
χ302-222-2-22-220-2-20020002i−2i2i−2i2i2i−2i−2i000000000000002-20000000000−22−2200−i2i2−i2i2
χ312-222-2-22-220-2-20020002i−2i2i−2i−2i−2i2i2i00000000000000-2200000000002−2−2200i2−i2−i2i2
χ322-222-2-22-220-2-20020002i−2i2i−2i−2i−2i2i2i00000000000000-220000000000−222−200−i2i2i2−i2
χ332-222-2-22-220-2-2002000−2i2i−2i2i2i2i−2i−2i00000000000000-2200000000002−2−2200−i2i2i2−i2
χ342-222-2-22-220-2-2002000−2i2i−2i2i2i2i−2i−2i00000000000000-220000000000−222−200i2−i2−i2i2
χ352-222-2-22-220-2-2002000−2i2i−2i2i−2i−2i2i2i000000000000002-200000000002−22−200−i2i2−i2i2
χ362-222-2-22-220-2-2002000−2i2i−2i2i−2i−2i2i2i000000000000002-20000000000−22−2200i2−i2i2−i2
χ372-22-22-2-22222-2-2-2-222-200002i−2i2i−2i0000000000002i−2i002-202i−2i000000000000000
χ382-22-22-2-22222-2-2-2-222-200002i−2i2i−2i0000000000002i−2i00-220−2i2i000000000000000
χ392-22-22-2-22222-2-2-2-222-20000−2i2i−2i2i000000000000−2i2i002-20−2i2i000000000000000
χ402-22-22-2-22222-2-2-2-222-20000−2i2i−2i2i000000000000−2i2i00-2202i−2i000000000000000
χ412-22-22-2-222-22-222-2-2-2200002i−2i2i−2i000000000000−2i2i00000002i−2i02-20000000000
χ422-22-22-2-222-22-222-2-2-2200002i−2i2i−2i000000000000−2i2i0000000−2i2i0-220000000000
χ432-22-22-2-222-22-222-2-2-220000−2i2i−2i2i0000000000002i−2i00000002i−2i0-220000000000
χ442-22-22-2-222-22-222-2-2-220000−2i2i−2i2i0000000000002i−2i0000000−2i2i02-20000000000
χ45444-4-44-4-440-4400-400000004-4-44000000000000000000000000000000000000
χ46444-4-44-4-440-4400-40000000-444-4000000000000000000000000000000000000
χ47444-4-44-4-4-404-4004000000000000000004i−4i0000000000000000000000000000
χ48444-4-44-4-4-404-400400000000000000000−4i4i0000000000000000000000000000
χ4944-4-4-4-44404004-40-40000000000000000002i2−2i22i2−2i2000000000000000000000000
χ5044-4-4-4-44404004-40-4000000000000000000−2i22i2−2i22i2000000000000000000000000
χ5144-4-4-4-4440-400-440400000000000000000022−22−2222000000000000000000000000
χ5244-4-4-4-4440-400-4404000000000000000000−222222−22000000000000000000000000
χ534-444-4-44-4-404400-40004i−4i−4i4i0000000000000000000000000000000000000000
χ544-444-4-44-4-404400-4000−4i4i4i−4i0000000000000000000000000000000000000000
χ554-44-44-4-44-44-44-4-444-4400000000000000000000000000000000000000000000
χ564-44-44-4-44-4-4-44444-44-400000000000000000000000000000000000000000000
χ574-4-44-44-440400-440-4000000000000004i−4i000000000000000000000000000000
χ584-4-44-44-440400-440-400000000000000−4i4i000000000000000000000000000000
χ594-4-44-44-440-4004-4040000000000004-400000000000000000000000000000000
χ604-4-44-44-440-4004-404000000000000-4400000000000000000000000000000000
χ6188-888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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