Finite Group Databasebeta

← Group #313755

Character table — Group #313755

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444442222448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1111111111111111-1-1-1-11-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11-11111-1-1-1-1-1-111-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-11111-1-11-1
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1111-1-111-1-11-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-11
χ91111111111111111-1-1-1-111111111-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-11111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-11-1-1111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-11-111-1-1-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1111-1-1-1-1-1-1111-1
χ17222222222-22-22-22-22222-2-2000000-2-20000220000-2-2000020000-20000000000
χ18222222222-22-22-22-22222-2-2000000-2-20000-2-20000220000-2000020000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000000220000220000-2-20000-2000020000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000000220000-2-2000022000020000-20000000000
χ2122222222-22-22-22-220000-2-22222220022-2-20000000000000-2-20000000000000
χ2222222222-22-22-22-220000-2-22222-2-200-2-2-2-20000000000000220000000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-22200-2-22200000000000002-20000000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-2-2-20022220000000000000-220000000000000
χ2522-2-2-22-220-202020-20000002i2i−2i−2i2i−2i002-200i2−i20000i2−i222−2−20000000000i2−i22−200
χ2622-2-2-22-220-202020-20000002i2i−2i−2i2i−2i002-200−i2i20000−i2i2−2−2220000000000−i2i2−2200
χ2722-2-2-22-220-202020-20000002i2i−2i−2i−2i2i00-2200i2−i20000i2−i222−2−20000000000−i2i2−2200
χ2822-2-2-22-220-202020-20000002i2i−2i−2i−2i2i00-2200−i2i20000−i2i2−2−2220000000000i2−i22−200
χ2922-2-2-22-220-202020-2000000−2i−2i2i2i2i−2i00-2200i2−i20000i2−i2−2−2220000000000−i2i22−200
χ3022-2-2-22-220-202020-2000000−2i−2i2i2i2i−2i00-2200−i2i20000−i2i222−2−20000000000i2−i2−2200
χ3122-2-2-22-220-202020-2000000−2i−2i2i2i−2i2i002-200i2−i20000i2−i2−2−2220000000000i2−i2−2200
χ3222-2-2-22-220-202020-2000000−2i−2i2i2i−2i2i002-200−i2i20000−i2i222−2−20000000000−i2i22−200
χ332-2-222-2-2222-2-222-2-222-2-2-222i−2i2i−2i002-2002i−2i002i2i−2i−2i0000000000000000000000
χ342-2-222-2-2222-2-222-2-222-2-2-22−2i2i−2i2i002-200−2i2i00−2i−2i2i2i0000000000000000000000
χ352-2-222-2-2222-2-222-2-2-2-222-222i−2i2i−2i00-22002i−2i00−2i−2i2i2i0000000000000000000000
χ362-2-222-2-2222-2-222-2-2-2-222-22−2i2i−2i2i00-2200−2i2i002i2i−2i−2i0000000000000000000000
χ372-2-222-2-222-2-222-2-2222-2-22-2000000-220000000000002i−2i2i−2i000000002i−2i000000
χ382-2-222-2-222-2-222-2-2222-2-22-2000000-22000000000000−2i2i−2i2i00000000−2i2i000000
χ392-2-222-2-222-2-222-2-22-2-2222-20000002-20000000000002i−2i2i−2i00000000−2i2i000000
χ402-2-222-2-222-2-222-2-22-2-2222-20000002-2000000000000−2i2i−2i2i000000002i−2i000000
χ412-2-222-2-22-222-2-222-200002-22i−2i2i−2i000000−2i2i0000000000000002i−2i02-200000000
χ422-2-222-2-22-222-2-222-200002-22i−2i2i−2i000000−2i2i000000000000000−2i2i0-2200000000
χ432-2-222-2-22-222-2-222-200002-2−2i2i−2i2i0000002i−2i0000000000000002i−2i0-2200000000
χ442-2-222-2-22-222-2-222-200002-2−2i2i−2i2i0000002i−2i000000000000000−2i2i02-200000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-44-4-4-440-40-40400000000000000000000022−2222−220000000000000000000000
χ47444-44-4-4-440-40-404000000000000000000000−2222−22220000000000000000000000
χ48444-44-4-4-4-404040-404-44-4000000000000000000000000000000000000000000
χ49444-44-4-4-4-404040-40-44-44000000000000000000000000000000000000000000
χ5044-4-4-44-44040-40-4040000000000000000002i2−2i20000−2i22i200000000000000000000
χ5144-4-4-44-44040-40-404000000000000000000−2i22i200002i2−2i200000000000000000000
χ524-44-4-4-44404040-40-4000000000000000000000000002i2−2i2−2i22i20000000000000000
χ534-44-4-4-44404040-40-400000000000000000000000000−2i22i22i2−2i20000000000000000
χ544-44-4-4-4440-40-404040000004-4-44000000000000000000000000000000000000
χ554-44-4-4-4440-40-40404000000-444-4000000000000000000000000000000000000
χ564-4-444-4-44-4-444-4-4440000-440000000000000000000000000000000000000000
χ574-4-4-4444-44040-40-40000000000000000000002i2−2i2−2i22i20000000000000000000000
χ584-4-4-4444-44040-40-4000000000000000000000−2i22i22i2−2i20000000000000000000000
χ594-4-4-4444-4-40-4040404-4-44000000000000000000000000000000000000000000
χ604-4-4-4444-4-40-404040-444-4000000000000000000000000000000000000000000
χ6188-88-8-88-8000000000000000000000000000000000000000000000000000000
χ628-888-88-8-8000000000000000000000000000000000000000000000000000000

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