Finite Group Databasebeta

← Group #268482

Character table — Group #268482

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444244444444444488888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ311111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11-11-1-1-1
χ411111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-111
χ5111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ6111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-11-11-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ9111111111111-1-1-1-11111-1-1-1-111-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11-1
χ10111111111111-1-1-1-11111-1-1-1-111-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-11
χ11111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-11-11
χ12111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-111-1
χ13111111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11-1
χ14111111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-111-1-11
χ15111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-11
χ16111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1
χ172222222222-2-2222222-2-222-2-2-2-2-2002200220000000000000000000000000000000-20-200
χ182222222222-2-2222222-2-222-2-2-2-2-200-2-200-2-2000000000000000000000000000000020200
χ192222222222-2-2-2-2-2-222-2-2-2-222-2-22002200-2-20000000000000000000000000000000-20200
χ202222222222-2-2-2-2-2-222-2-2-2-222-2-2200-2-20022000000000000000000000000000000020-200
χ2122222222-2-2222222-2-222-2-222-2-2-222002200000000000000000000000000000000-20-2000
χ2222222222-2-2222222-2-222-2-222-2-2-2-2-200-2-200000000000000000000000000000000202000
χ2322222222-2-222-2-2-2-2-2-22222-2-2-2-222200-2-200000000000000000000000000000000-202000
χ2422222222-2-222-2-2-2-2-2-22222-2-2-2-22-2-200220000000000000000000000000000000020-2000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-22220000000022-2-20000000000000000000000002-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-222200000000-2-222000000000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000022-2-2000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000-2-2220000000000000000000000002-2000000
χ292-22-22-22-2002-22i2i−2i−2i002-2002i−2i0002i−2i002-200000022−2−2i2i2−i2−i200000000i2i2−i2−i222−2−200000000
χ302-22-22-22-2002-22i2i−2i−2i002-2002i−2i0002i−2i002-2000000−2−222−i2−i2i2i200000000−i2−i2i2i2−2−22200000000
χ312-22-22-22-2002-22i2i−2i−2i002-2002i−2i000−2i2i00-2200000022−2−2i2i2−i2−i200000000−i2−i2i2i2−2−22200000000
χ322-22-22-22-2002-22i2i−2i−2i002-2002i−2i000−2i2i00-22000000−2−222−i2−i2i2i200000000i2i2−i2−i222−2−200000000
χ332-22-22-22-2002-2−2i−2i2i2i002-200−2i2i0002i−2i00-2200000022−2−2−i2−i2i2i200000000i2i2−i2−i2−2−22200000000
χ342-22-22-22-2002-2−2i−2i2i2i002-200−2i2i0002i−2i00-22000000−2−222i2i2−i2−i200000000−i2−i2i2i222−2−200000000
χ352-22-22-22-2002-2−2i−2i2i2i002-200−2i2i000−2i2i002-200000022−2−2−i2−i2i2i200000000−i2−i2i2i222−2−200000000
χ362-22-22-22-2002-2−2i−2i2i2i002-200−2i2i000−2i2i002-2000000−2−222i2i2−i2−i200000000i2i2−i2−i2−2−22200000000
χ372-2-22-222-22-2002i−2i2i−2i2-2002i−2i00000002i−2i002-200000000000022−2−2i2i2−i2−i2i2−i2i2−i22−22−200000000
χ382-2-22-222-22-2002i−2i2i−2i2-2002i−2i00000002i−2i002-2000000000000−2−222−i2−i2i2i2−i2i2−i2i2−22−2200000000
χ392-2-22-222-22-2002i−2i2i−2i2-2002i−2i0000000−2i2i00-2200000000000022−2−2i2i2−i2−i2−i2i2−i2i2−22−2200000000
χ402-2-22-222-22-2002i−2i2i−2i2-2002i−2i0000000−2i2i00-22000000000000−2−222−i2−i2i2i2i2−i2i2−i22−22−200000000
χ412-2-22-222-22-200−2i2i−2i2i2-200−2i2i00000002i−2i00-2200000000000022−2−2−i2−i2i2i2i2−i2i2−i2−22−2200000000
χ422-2-22-222-22-200−2i2i−2i2i2-200−2i2i00000002i−2i00-22000000000000−2−222i2i2−i2−i2−i2i2−i2i22−22−200000000
χ432-2-22-222-22-200−2i2i−2i2i2-200−2i2i0000000−2i2i002-200000000000022−2−2−i2−i2i2i2−i2i2−i2i22−22−200000000
χ442-2-22-222-22-200−2i2i−2i2i2-200−2i2i0000000−2i2i002-2000000000000−2−222i2i2−i2−i2i2−i2i2−i2−22−2200000000
χ452-2-2-222-2222220000-2-2-2-200002-20000000002-22-200002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ462-2-2-222-2222220000-2-2-2-200002-20000000002-22-20000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ472-2-2-222-2222220000-2-2-2-200002-2000000000-22-2200002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ482-2-2-222-2222220000-2-2-2-200002-2000000000-22-220000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ492-2-2-222-22-2-2-2-20000222200002-20000000002-2-222-22-200002-22-200000000000000000000
χ502-2-2-222-22-2-2-2-20000222200002-20000000002-2-22-22-220000-22-2200000000000000000000
χ512-2-2-222-22-2-2-2-20000222200002-2000000000-222-22-22-20000-22-2200000000000000000000
χ522-2-2-222-22-2-2-2-20000222200002-2000000000-222-2-22-2200002-22-200000000000000000000
χ53444-4-44-4-44-4000000-4400000000000000000000000000000000022−22−22220000000000000000
χ54444-4-44-4-44-4000000-44000000000000000000000000000000000−222222−220000000000000000
χ55444-4-44-4-4-440000004-40000000000000000000000000000022−22−222200000000000000000000
χ56444-4-44-4-4-440000004-400000000000000000000000000000−222222−2200000000000000000000
χ5744-444-4-4-4004-4000000-440000000000000000000000022−22−2222000000000000000000000000
χ5844-444-4-4-4004-4000000-4400000000000000000000000−222222−22000000000000000000000000
χ5944-444-4-4-400-440000004-4000000000000000000022−22−22220000000000000000000000000000
χ6044-444-4-4-400-440000004-40000000000000000000−222222−220000000000000000000000000000
χ6144-4-4-4-44400004-4-440000000000000000000000000000000000000002-2-222-2-2200000000
χ6244-4-4-4-44400004-4-44000000000000000000000000000000000000000-222-2-222-200000000
χ6344-4-4-4-4440000-444-40000000000000000000000000000000000000002-2-22-222-200000000
χ6444-4-4-4-4440000-444-4000000000000000000000000000000000000000-222-22-2-2200000000
χ654-44-44-44-400-444i4i−4i−4i00-4400−4i4i00000000000000000000000000000000000000000000000
χ664-44-44-44-400-44−4i−4i4i4i00-44004i−4i00000000000000000000000000000000000000000000000
χ674-4-44-444-4-44004i−4i4i−4i-4400−4i4i0000000000000000000000000000000000000000000000000
χ684-4-44-444-4-4400−4i4i−4i4i-44004i−4i0000000000000000000000000000000000000000000000000
χ694-4-4-444-4444-4-40000-4-4440000-44000000000000000000000000000000000000000000000
χ704-4-4-444-44-4-444000044-4-40000-44000000000000000000000000000000000000000000000
χ718-888-8-8-88000000000000000000000000000000000000000000000000000000000000000

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