Finite Group Databasebeta

← Group #282829

Character table — Group #282829

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222244444488888888888888224444448888882
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-1-11-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-1-1-11-1-1111-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111111-1-1-111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1111-1-111-1-111-1
χ172222222222-22-2-2-222222-2-2000000220000-2-200-2-2000022000000-2000000000000
χ182222222222-22-2-2-222222-2-2000000-2-20000-2-200220000-2-20000002000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-20000002200002200220000-2-2000000-2000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-2000000-2-200002200-2-20000220000002000000000000
χ2122222222-2-22-2222-20000-2-222222200-2-2-2-200-2-2000000000000000002000000000
χ2222222222-2-22-2222-20000-2-22222-2-200222200-2-200000000000000000-2000000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-2220022-2-2002200000000000000000-2000000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-2-2-200-2-2220022000000000000000002000000000
χ2522-22-22-2-22-202000-22i2i−2i−2i0022−2−2002-20000002−200i2i2−i2−i22i−2ii2i2−i2−i2000000002−200000
χ2622-22-22-2-22-202000-22i2i−2i−2i0022−2−200-220000002−200i2i2−i2−i2−2i2i−i2−i2i2i200000000−2200000
χ2722-22-22-2-22-202000-22i2i−2i−2i00−2−222002-2000000−2200−i2−i2i2i22i−2i−i2−i2i2i200000000−2200000
χ2822-22-22-2-22-202000-22i2i−2i−2i00−2−22200-22000000−2200−i2−i2i2i2−2i2ii2i2−i2−i2000000002−200000
χ2922-22-22-2-22-202000-2−2i−2i2i2i0022−2−2002-20000002−200−i2−i2i2i2−2i2i−i2−i2i2i2000000002−200000
χ3022-22-22-2-22-202000-2−2i−2i2i2i0022−2−200-220000002−200−i2−i2i2i22i−2ii2i2−i2−i200000000−2200000
χ3122-22-22-2-22-202000-2−2i−2i2i2i00−2−222002-2000000−2200i2i2−i2−i2−2i2ii2i2−i2−i200000000−2200000
χ3222-22-22-2-22-202000-2−2i−2i2i2i00−2−22200-22000000−2200i2i2−i2−i22i−2i−i2−i2i2i2000000002−200000
χ332-2-222-2-22222-2-2-22-22i−2i2i−2i2-200002-200002-22i−2i000000000000000002i−2i0000000000
χ342-2-222-2-22222-2-2-22-22i−2i2i−2i2-20000-220000-222i−2i00000000000000000−2i2i0000000000
χ352-2-222-2-22222-2-2-22-2−2i2i−2i2i2-200002-200002-2−2i2i00000000000000000−2i2i0000000000
χ362-2-222-2-22222-2-2-22-2−2i2i−2i2i2-20000-220000-22−2i2i000000000000000002i−2i0000000000
χ372-2-222-2-2222-2-222-2-22i−2i2i−2i-22000000000000−2i2i000000000000002-2000000002i−2i000
χ382-2-222-2-2222-2-222-2-22i−2i2i−2i-22000000000000−2i2i00000000000000-2200000000−2i2i000
χ392-2-222-2-2222-2-222-2-2−2i2i−2i2i-220000000000002i−2i000000000000002-200000000−2i2i000
χ402-2-222-2-2222-2-222-2-2−2i2i−2i2i-220000000000002i−2i00000000000000-22000000002i−2i000
χ412-2-222-2-22-2-222-2-2220000-2200002-20000-220000002-22-20000000000002-20000000
χ422-2-222-2-22-2-222-2-2220000-2200002-20000-22000000-22-22000000000000-220000000
χ432-2-222-2-22-2-222-2-2220000-220000-2200002-20000002-22-2000000000000-220000000
χ442-2-222-2-22-2-222-2-2220000-220000-2200002-2000000-22-220000000000002-20000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ4644-44-44-4-4-440-400040000002222−22−220000000000−2222000000000000000000000000000
χ4744-44-44-4-4-440-40004000000−22−222222000000000022−22000000000000000000000000000
χ4844-4-44-44-400404-4-4000000000000000000000000000000000000000000000002i2−2i20
χ4944-4-44-44-400404-4-400000000000000000000000000000000000000000000000−2i22i20
χ5044-4-44-44-400-40-4440000000000000004-4000000000000000000000000000000000
χ5144-4-44-44-400-40-444000000000000000-44000000000000000000000000000000000
χ524-444-4-44-44-40-400044-4-44000000000000000000000000000000000000000000000
χ534-444-4-44-44-40-40004-444-4000000000000000000000000000000000000000000000
χ544-444-4-44-4-4404000-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ554-444-4-44-4-4404000-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ564-44-444-4-40040-44-400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ574-44-444-4-40040-44-40000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ584-44-444-4-400-404-4400000004-44-4000000000000000000000000000000000000000
χ594-44-444-4-400-404-440000000-44-44000000000000000000000000000000000000000
χ604-4-444-4-44-4-4-4444-4400004-40000000000000000000000000000000000000000000
χ614-4-4-4-44440000000000000022−22−222200000000000022−220000002-2-22000000000000000
χ624-4-4-4-44440000000000000022−22−2222000000000000−2222000000-222-2000000000000000
χ634-4-4-4-444400000000000000−222222−2200000000000022−22000000-222-2000000000000000
χ644-4-4-4-444400000000000000−222222−22000000000000−22220000002-2-22000000000000000
χ65888-8-8-8-88000000000000000000000000000000000000000000000000000000000

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