Finite Group Databasebeta

← Group #329607

Character table — Group #329607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444442244444444224444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1-11
χ121111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-2222-2-222-2-222-2-2-2-20000000022-2-222-2-200000000000000000000
χ18222222222-2-2222-2-222-2-222-2-2-2-200000000-2-222-2-22200000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-222220000000022-2-2-2-22200000000000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-2222200000000-2-22222-2-200000000000000000000
χ2122222222-222-2-2-22222-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ2222222222-222-2-2-22222-2-2-2-2-2-222-2-22222-2-20000000000000000000000000000
χ2322222222-222-2-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000
χ2422222222-222-2-2-222-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292-2-222-2-22022000-2-22-20000002-2002i−2i2i−2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ302-2-222-2-22022000-2-22-20000002-2002i−2i2i−2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ312-2-222-2-22022000-2-22-20000002-200−2i2i−2i2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ322-2-222-2-22022000-2-22-20000002-200−2i2i−2i2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ332-2-222-2-22022000-2-2-22000000-22002i−2i−2i2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ342-2-222-2-22022000-2-2-22000000-22002i−2i−2i2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ352-2-222-2-22022000-2-2-22000000-2200−2i2i2i−2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ362-2-222-2-22022000-2-2-22000000-2200−2i2i2i−2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ372-2-222-2-220-2-2000222-2000000-222-200002-22−2−222−2−222−2−222−2−22000000000000
χ382-2-222-2-220-2-2000222-2000000-222-200002-2−222−2−222−2−222−2−222−2000000000000
χ392-2-222-2-220-2-2000222-2000000-22-220000-222−2−222−2−22−222−2−222−2000000000000
χ402-2-222-2-220-2-2000222-2000000-22-220000-22−222−2−222−22−2−222−2−22000000000000
χ412-2-222-2-220-2-200022-220000002-22-20000-222−2−22−222−22−2−22−222−2000000000000
χ422-2-222-2-220-2-200022-220000002-22-20000-22−222−22−2−22−222−22−2−22000000000000
χ432-2-222-2-220-2-200022-220000002-2-2200002-22−2−22−222−2−222−22−2−22000000000000
χ442-2-222-2-220-2-200022-220000002-2-2200002-2−222−22−2−222−2−22−222−2000000000000
χ45444-4-4-4-4404-40004-400004i−4i4i−4i00000000000000000000000000000000000000
χ46444-4-4-4-4404-40004-40000−4i4i−4i4i00000000000000000000000000000000000000
χ47444-4-4-4-440-44000-4400004i−4i−4i4i00000000000000000000000000000000000000
χ48444-4-4-4-440-44000-440000−4i4i4i−4i00000000000000000000000000000000000000
χ4944-44-44-4-44004-4-4000000000000000000000000000000000000000022−22000000
χ5044-44-44-4-44004-4-40000000000000000000000000000000000000000−2222000000
χ5144-44-44-4-4-400-4440000000000000000000000000000000000000000002i2−2i20000
χ5244-44-44-4-4-400-444000000000000000000000000000000000000000000−2i22i20000
χ534-44-444-4-4400-44-400000000000000000000000000000000000022−220000000000
χ544-44-444-4-4400-44-4000000000000000000000000000000000000−22220000000000
χ554-44-444-4-4-4004-44000000000000000000000000000000000000002i2−2i200000000
χ564-44-444-4-4-4004-4400000000000000000000000000000000000000−2i22i200000000
χ574-4-4-4-444444-4-4-44-44004-4000000000000000000000000000000000000000000
χ584-4-4-4-44444-44-4-444-400-44000000000000000000000000000000000000000000
χ594-4-4-4-4444-44-444-4-4400-44000000000000000000000000000000000000000000
χ604-4-4-4-4444-4-4444-44-4004-4000000000000000000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-888-8-88-8000000000000000000000000000000000000000000000000000000

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