Finite Group Databasebeta

← Group #336808

Character table — Group #336808

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111111111-11-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-11
χ61111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-111-1-111-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-111111-11
χ9111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-111
χ11111111111111111111-1-1-1-11111-1-11111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-111
χ12111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-11-1-111-1-111-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111111111111-1-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-11111-1
χ172222222222-2-2-2-222-2-2000022220000002222-2-2000000-2-200000000-20000000000
χ182222222222-2-2-2-222-2-200002222000000-2-2-2-222000000-2-20000000020000000000
χ192222222222-2-2-2-222-2-20000-2-2-2-200000022-2-2-2-2000000220000000020000000000
χ202222222222-2-2-2-222-2-20000-2-2-2-2000000-2-222220000002200000000-20000000000
χ2122222222-2-22222-2-2-2-22222000022-2-222000000-2-2000000000000000-2000000000
χ2222222222-2-22222-2-2-2-222220000-2-222-2-2000000-2-20000000000000002000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200002222-2-200000022000000000000000-2000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-20000-2-2-2-222000000220000000000000002000000000
χ2522-2-2-2-2222-200002-200i2i2−i2−i22i2i−2i−2i0000002i−2i2-200i2−i222−2−200000022−2−20000i2−i200000
χ2622-2-2-2-2222-200002-200i2i2−i2−i22i2i−2i−2i000000−2i2i-2200i2−i2−2−22200000022−2−20000−i2i200000
χ2722-2-2-2-2222-200002-200i2i2−i2−i2−2i−2i2i2i0000002i−2i-2200i2−i222−2−2000000−2−2220000−i2i200000
χ2822-2-2-2-2222-200002-200i2i2−i2−i2−2i−2i2i2i000000−2i2i2-200i2−i2−2−222000000−2−2220000i2−i200000
χ2922-2-2-2-2222-200002-200−i2−i2i2i22i2i−2i−2i0000002i−2i2-200−i2i2−2−222000000−2−2220000−i2i200000
χ3022-2-2-2-2222-200002-200−i2−i2i2i22i2i−2i−2i000000−2i2i-2200−i2i222−2−2000000−2−2220000i2−i200000
χ3122-2-2-2-2222-200002-200−i2−i2i2i2−2i−2i2i2i0000002i−2i-2200−i2i2−2−22200000022−2−20000i2−i200000
χ3222-2-2-2-2222-200002-200−i2−i2i2i2−2i−2i2i2i000000−2i2i2-200−i2i222−2−200000022−2−20000−i2i200000
χ332-22-22-22-2-2-222-2-2222-200000000000000000000002i−2i2i−2i0022-2-20000002i−2i0000000
χ342-22-22-22-2-2-222-2-2222-200000000000000000000002i−2i2i−2i00-2-222000000−2i2i0000000
χ352-22-22-22-2-2-222-2-2222-20000000000000000000000−2i2i−2i2i0022-2-2000000−2i2i0000000
χ362-22-22-22-2-2-222-2-2222-20000000000000000000000−2i2i−2i2i00-2-2220000002i−2i0000000
χ372-22-2-22-22002-22-200002-22-2i2−i2i2−i22i−2i002i−2i000000000000i2−i22−22−2i2−i2i2−i20000002−2000
χ382-22-2-22-22002-22-200002-22-2i2−i2i2−i2−2i2i00−2i2i000000000000i2−i2−22−22i2−i2i2−i2000000−22000
χ392-22-2-22-22002-22-200002-22-2−i2i2−i2i22i−2i002i−2i000000000000−i2i2−22−22−i2i2−i2i2000000−22000
χ402-22-2-22-22002-22-200002-22-2−i2i2−i2i2−2i2i00−2i2i000000000000−i2i22−22−2−i2i2−i2i20000002−2000
χ412-22-2-22-22002-22-20000-22-22i2−i2i2−i22i−2i00−2i2i000000000000i2−i2−22−22−i2i2−i2i20000002−2000
χ422-22-2-22-22002-22-20000-22-22i2−i2i2−i2−2i2i002i−2i000000000000i2−i22−22−2−i2i2−i2i2000000−22000
χ432-22-2-22-22002-22-20000-22-22−i2i2−i2i22i−2i00−2i2i000000000000−i2i22−22−2i2−i2i2−i2000000−22000
χ442-22-2-22-22002-22-20000-22-22−i2i2−i2i2−2i2i002i−2i000000000000−i2i2−22−22i2−i2i2−i20000002−2000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ464444-4-4-4-4004-4-440000000000000000000000000000000022−22−2222000000000000000
χ474444-4-4-4-4004-4-4400000000000000000000000000000000−222222−22000000000000000
χ484444-4-4-4-400-444-4000000000000004-400000000000000000000000000000000000
χ494444-4-4-4-400-444-400000000000000-4400000000000000000000000000000000000
χ5044-4-4-4-444-440000-44002i22i2−2i2−2i20000000000000000−2i22i20000000000000000000000000
χ5144-4-4-4-444-440000-4400−2i2−2i22i22i200000000000000002i2−2i20000000000000000000000000
χ524-44-44-44-44444-4-4-4-4-4400000000000000000000000000000000000000000000000
χ534-44-44-44-444-4-444-4-44-400000000000000000000000000000000000000000000000
χ544-44-44-44-4-4-4-4-44444-4400000000000000000000000000000000000000000000000
χ554-44-4-44-4400-44-44000000002i2−2i22i2−2i2000000000000000000−2i22i20000000000000000000
χ564-44-4-44-4400-44-4400000000−2i22i2−2i22i20000000000000000002i2−2i20000000000000000000
χ574-4-444-4-4400000000002i2−2i2−2i22i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ584-4-444-4-4400000000002i2−2i2−2i22i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ594-4-444-4-440000000000−2i22i22i2−2i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ604-4-444-4-440000000000−2i22i22i2−2i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ614-4-44-444-44-40000-44000000000000000000004i−4i000000000000000000000000000
χ624-4-44-444-44-40000-4400000000000000000000−4i4i000000000000000000000000000
χ634-4-44-444-4-4400004-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ644-4-44-444-4-4400004-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ6588-8-888-8-8000000000000000000000000000000000000000000000000000000000

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