Finite Group Databasebeta

← Group #333718

Character table — Group #333718

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888844448888244
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-11-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-11-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-111-1-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-11
χ9111111111111111111-1-1-1-1111111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-1-1-1111-1-1
χ11111111111111111111-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11111-111
χ13111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-11111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11
χ17222222222-2-22-2-222-2-200002222000022-2-2220000-2-2000000000000000-20000000
χ18222222222-2-22-2-222-2-2000022220000-2-222-2-20000-2-200000000000000020000000
χ19222222222-2-22-2-222-2-20000-2-2-2-2000022-2-2-2-200002200000000000000020000000
χ20222222222-2-22-2-222-2-20000-2-2-2-20000-2-22222000022000000000000000-20000000
χ2122222222-222-222-2-2-2-22222000022-2-2000000-2-2-2-20000000000000000200000000
χ2222222222-222-222-2-2-2-222220000-2-22200000022-2-20000000000000000-200000000
χ2322222222-222-222-2-2-2-2-2-2-2-200002222000000-2-2220000000000000000-200000000
χ2422222222-222-222-2-2-2-2-2-2-2-20000-2-2-2-200000022220000000000000000200000000
χ2522-2-22-2-22200200-2-20022−2−22i2i−2i−2i00002-2002i−2i002−20022−2−20000i2i2−i2−i2000000i2−i2000
χ2622-2-22-2-22200200-2-20022−2−22i2i−2i−2i0000-2200−2i2i002−200−2−2220000i2i2−i2−i2000000−i2i2000
χ2722-2-22-2-22200200-2-20022−2−2−2i−2i2i2i00002-200−2i2i002−20022−2−20000−i2−i2i2i2000000−i2i2000
χ2822-2-22-2-22200200-2-20022−2−2−2i−2i2i2i0000-22002i−2i002−200−2−2220000−i2−i2i2i2000000i2−i2000
χ2922-2-22-2-22200200-2-200−2−2222i2i−2i−2i00002-2002i−2i00−2200−2−2220000−i2−i2i2i2000000−i2i2000
χ3022-2-22-2-22200200-2-200−2−2222i2i−2i−2i0000-2200−2i2i00−220022−2−20000−i2−i2i2i2000000i2−i2000
χ3122-2-22-2-22200200-2-200−2−222−2i−2i2i2i00002-200−2i2i00−2200−2−2220000i2i2−i2−i2000000i2−i2000
χ3222-2-22-2-22200200-2-200−2−222−2i−2i2i2i0000-22002i−2i00−220022−2−20000i2i2−i2−i2000000−i2i2000
χ332-2-2222-2-202-202-200002i−2i2i−2ii2−i2i2−i2002-20000002i−2i00i2−i2000022−2−22−22−20000i2−i200000
χ342-2-2222-2-202-202-200002i−2i2i−2ii2−i2i2−i200-22000000−2i2i00i2−i20000−2−2222−22−20000−i2i200000
χ352-2-2222-2-202-202-200002i−2i2i−2i−i2i2−i2i2002-20000002i−2i00−i2i20000−2−222−22−220000−i2i200000
χ362-2-2222-2-202-202-200002i−2i2i−2i−i2i2−i2i200-22000000−2i2i00−i2i2000022−2−2−22−220000i2−i200000
χ372-2-2222-2-202-202-20000−2i2i−2i2ii2−i2i2−i2002-2000000−2i2i00i2−i20000−2−222−22−220000i2−i200000
χ382-2-2222-2-202-202-20000−2i2i−2i2ii2−i2i2−i200-220000002i−2i00i2−i2000022−2−2−22−220000−i2i200000
χ392-2-2222-2-202-202-20000−2i2i−2i2i−i2i2−i2i2002-2000000−2i2i00−i2i2000022−2−22−22−20000−i2i200000
χ402-2-2222-2-202-202-20000−2i2i−2i2i−i2i2−i2i200-220000002i−2i00−i2i20000−2−2222−22−20000i2−i200000
χ412-2-22-2-222-2-2-2222-22-220000000000000000000000002-22-22-22-200002-2000000000
χ422-2-22-2-222-2-2-2222-22-220000000000000000000000002-22-2-22-220000-22000000000
χ432-2-22-2-222-2-2-2222-22-22000000000000000000000000-22-222-22-20000-22000000000
χ442-2-22-2-222-2-2-2222-22-22000000000000000000000000-22-22-22-2200002-2000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ464444-4-4-4-404-40-440000000000004-40000000000000000000000000000000000000
χ474444-4-4-4-404-40-44000000000000-440000000000000000000000000000000000000
χ484444-4-4-4-40-4404-40000000000000000000000000000000022−22−2222000000000000000
χ494444-4-4-4-40-4404-400000000000000000000000000000000−222222−22000000000000000
χ5044-4-44-4-44-400-40044002222−22−220000000000000000−22220000000000000000000000000
χ5144-4-44-4-44-400-4004400−22−222222000000000000000022−220000000000000000000000000
χ524-44-44-44-400000000002i2−2i2−2i22i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ534-44-44-44-400000000002i2−2i2−2i22i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ544-44-44-44-40000000000−2i22i22i2−2i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ554-44-44-44-40000000000−2i22i22i2−2i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ564-44-4-44-44400-400-4400000000000000004-40000000000000000000000000000000
χ574-44-4-44-44400-400-440000000000000000-440000000000000000000000000000000
χ584-44-4-44-44-4004004-40000000000000000000000000022−22−22220000000000000000000
χ594-44-4-44-44-4004004-400000000000000000000000000−222222−220000000000000000000
χ604-4-4444-4-40-440-44000000002i2−2i22i2−2i200000000000000−2i22i200000000000000000000000
χ614-4-4444-4-40-440-4400000000−2i22i2−2i22i2000000000000002i2−2i200000000000000000000000
χ624-4-44-4-444444-4-4-44-4-4400000000000000000000000000000000000000000000000
χ634-4-44-4-4444-4-4-4444-44-400000000000000000000000000000000000000000000000
χ644-4-44-4-444-4444-4-4-444-400000000000000000000000000000000000000000000000
χ6588-8-8-888-8000000000000000000000000000000000000000000000000000000000

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