Finite Group Databasebeta

← Group #268402

Character table — Group #268402

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444222224444444488888888888888888888888824444444
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
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111
χ5111111111111111111111111111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ8111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-11-1-11-1-1
χ9111111111111-1-1-1-11111-1-1-1-111-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-11-1
χ10111111111111-1-1-1-11111-1-1-1-111-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-1-1-1-11
χ11111111111111-1-1-1-11111-1-1-1-111-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11-11
χ12111111111111-1-1-1-11111-1-1-1-111-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-111-1
χ13111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-11
χ14111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11111-1
χ15111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-11-1
χ16111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-1111-1-11
χ172222222222-2-2222222-2-2-2-222-2-2-2000022002200000000000000000000000000-2-2000000
χ182222222222-2-2222222-2-2-2-222-2-2-20000-2-200-2-20000000000000000000000000022000000
χ192222222222-2-2-2-2-2-222-2-222-2-2-2-2200002200-2-2000000000000000000000000002-2000000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-220000-2-2002200000000000000000000000000-22000000
χ2122222222-2-2222222-2-22222-2-2-2-2-200000022002200000000000000000000000000-200-200
χ2222222222-2-2222222-2-22222-2-2-2-2-2000000-2-200-2-200000000000000000000000000200200
χ2322222222-2-222-2-2-2-2-2-222-2-222-2-220000002200-2-200000000000000000000000000-200200
χ2422222222-2-222-2-2-2-2-2-222-2-222-2-22000000-2-2002200000000000000000000000000200-200
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-222222-2-2000000000000000000000000000000000002-2000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2222-2-22200000000000000000000000000000000000-22000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-222-2-200000000000000000000000000000000000-22000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-222000000000000000000000000000000000002-2000
χ2922-2-2-222-2002-22i2i−2i−2i002-22i−2i000000000002i−2i002-200000000i2i2−i2−i222−2−222−2−2i2i2−i2−i200000000
χ3022-2-2-222-2002-22i2i−2i−2i002-22i−2i000000000002i−2i002-200000000−i2−i2i2i2−2−222−2−222−i2−i2i2i200000000
χ3122-2-2-222-2002-22i2i−2i−2i002-22i−2i00000000000−2i2i00-2200000000i2i2−i2−i222−2−2−2−222−i2−i2i2i200000000
χ3222-2-2-222-2002-22i2i−2i−2i002-22i−2i00000000000−2i2i00-2200000000−i2−i2i2i2−2−22222−2−2i2i2−i2−i200000000
χ3322-2-2-222-2002-2−2i−2i2i2i002-2−2i2i000000000002i−2i00-2200000000i2i2−i2−i2−2−22222−2−2−i2−i2i2i200000000
χ3422-2-2-222-2002-2−2i−2i2i2i002-2−2i2i000000000002i−2i00-2200000000−i2−i2i2i222−2−2−2−222i2i2−i2−i200000000
χ3522-2-2-222-2002-2−2i−2i2i2i002-2−2i2i00000000000−2i2i002-200000000i2i2−i2−i2−2−222−2−222i2i2−i2−i200000000
χ3622-2-2-222-2002-2−2i−2i2i2i002-2−2i2i00000000000−2i2i002-200000000−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000
χ372-22-222-2-22-2002i−2i2i−2i2-200002i−2i00000002-2002i−2i0022−2−2i2i2−i2−i2000000002−22−2i2−i2i2−i200000000
χ382-22-222-2-22-2002i−2i2i−2i2-200002i−2i00000002-2002i−2i00−2−222−i2−i2i2i200000000−22−22−i2i2−i2i200000000
χ392-22-222-2-22-2002i−2i2i−2i2-200002i−2i0000000-2200−2i2i0022−2−2i2i2−i2−i200000000−22−22−i2i2−i2i200000000
χ402-22-222-2-22-2002i−2i2i−2i2-200002i−2i0000000-2200−2i2i00−2−222−i2−i2i2i2000000002−22−2i2−i2i2−i200000000
χ412-22-222-2-22-200−2i2i−2i2i2-20000−2i2i00000002-200−2i2i0022−2−2−i2−i2i2i2000000002−22−2−i2i2−i2i200000000
χ422-22-222-2-22-200−2i2i−2i2i2-20000−2i2i00000002-200−2i2i00−2−222i2i2−i2−i200000000−22−22i2−i2i2−i200000000
χ432-22-222-2-22-200−2i2i−2i2i2-20000−2i2i0000000-22002i−2i0022−2−2−i2−i2i2i200000000−22−22i2−i2i2−i200000000
χ442-22-222-2-22-200−2i2i−2i2i2-20000−2i2i0000000-22002i−2i00−2−222i2i2−i2−i2000000002−22−2−i2i2−i2i200000000
χ452-22-2-2-22222220000-2-2-2-200002-202-22-20000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ462-22-2-2-22222220000-2-2-2-200002-202-22-2000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ472-22-2-2-22222220000-2-2-2-200002-20-22-220000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ482-22-2-2-22222220000-2-2-2-200002-20-22-22000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ492-22-2-2-222-2-2-2-20000222200002-202-2-22000000002-22-200002-22-200000000000000000000
χ502-22-2-2-222-2-2-2-20000222200002-202-2-2200000000-22-220000-22-2200000000000000000000
χ512-22-2-2-222-2-2-2-20000222200002-20-222-2000000002-22-20000-22-2200000000000000000000
χ522-22-2-2-222-2-2-2-20000222200002-20-222-200000000-22-2200002-22-200000000000000000000
χ534444-4-4-4-44-4000000-44000000000000000000000000022−22−2222000000000000000000000000
χ544444-4-4-4-44-4000000-440000000000000000000000000−222222−22000000000000000000000000
χ554444-4-4-4-4-440000004-400000000000000000000022−22−22220000000000000000000000000000
χ564444-4-4-4-4-440000004-4000000000000000000000−222222−220000000000000000000000000000
χ5744-4-4-444-400-444i4i−4i−4i00-44−4i4i0000000000000000000000000000000000000000000000000
χ5844-4-4-444-400-44−4i−4i4i4i00-444i−4i0000000000000000000000000000000000000000000000000
χ594-44-444-4-4-44004i−4i4i−4i-440000−4i4i00000000000000000000000000000000000000000000000
χ604-44-444-4-4-4400−4i4i−4i4i-4400004i−4i00000000000000000000000000000000000000000000000
χ614-44-4-4-44444-4-40000-4-4440000-44000000000000000000000000000000000000000000000
χ624-44-4-4-444-4-444000044-4-40000-44000000000000000000000000000000000000000000000
χ634-4-444-44-4004-4000000-4400000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ644-4-444-44-4004-4000000-440000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ654-4-444-44-400-440000004-40000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ664-4-444-44-400-440000004-4000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ674-4-44-44-4400004-4-440000000000000000000000000000000000000002-2-222-2-2200000000
χ684-4-44-44-4400004-4-44000000000000000000000000000000000000000-222-2-222-200000000
χ694-4-44-44-440000-444-40000000000000000000000000000000000000002-2-22-222-200000000
χ704-4-44-44-440000-444-4000000000000000000000000000000000000000-222-22-2-2200000000
χ7188-8-88-8-88000000000000000000000000000000000000000000000000000000000000000

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