Finite Group Databasebeta

← Group #314211

Character table — Group #314211

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ71111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1111-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-111-1-1-1-11-1-1-111-1-1-1-111-11
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1111-1-1-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-111111-1-1-11111-1-1-1-11-1
χ13111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-111111-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-11-1-1111111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11-111-1-1-1-111111-1
χ17222222222-22-22-22-2-2-200002222-2-200-2-20000220000-2-2000000000000000000
χ18222222222-22-22-22-2-2-2000022-2-2-2-200220000-2-2000022000000000000000000
χ19222222222-22-22-22-2-2-20000-2-2222200-2-20000-2-2000022000000000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-22200220000220000-2-2000000000000000000
χ2122222222-22-22-22-22-2-22222000000220022-2-2000000000000-2-2000000000000
χ2222222222-22-22-22-22-2-22222000000-2-200-2-2-2-200000000000022000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000002200-2-2220000000000002-2000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000-2-2002222000000000000-22000000000000
χ252-22-22-2-2202020-20-2002i2i−2i−2i0000002i−2i002-2002−200002−2i2i2−i2−i2000000i2−i2002−200
χ262-22-22-2-2202020-20-2002i2i−2i−2i0000002i−2i002-200−220000−22−i2−i2i2i2000000−i2i200−2200
χ272-22-22-2-2202020-20-2002i2i−2i−2i000000−2i2i00-22002−200002−2i2i2−i2−i2000000−i2i200−2200
χ282-22-22-2-2202020-20-2002i2i−2i−2i000000−2i2i00-2200−220000−22−i2−i2i2i2000000i2−i2002−200
χ292-22-22-2-2202020-20-200−2i−2i2i2i0000002i−2i00-22002−200002−2−i2−i2i2i2000000i2−i200−2200
χ302-22-22-2-2202020-20-200−2i−2i2i2i0000002i−2i00-2200−220000−22i2i2−i2−i2000000−i2i2002−200
χ312-22-22-2-2202020-20-200−2i−2i2i2i000000−2i2i002-2002−200002−2−i2−i2i2i2000000−i2i2002−200
χ322-22-22-2-2202020-20-200−2i−2i2i2i000000−2i2i002-200−220000−22i2i2−i2−i2000000i2−i200−2200
χ332-2-2-2222-222-2-222-2-2-222i−2i2i−2i2-2002-20000002i−2i000000000000000000002i−2i0000
χ342-2-2-2222-222-2-222-2-2-222i−2i2i−2i-2200-220000002i−2i00000000000000000000−2i2i0000
χ352-2-2-2222-222-2-222-2-2-22−2i2i−2i2i2-2002-2000000−2i2i00000000000000000000−2i2i0000
χ362-2-2-2222-222-2-222-2-2-22−2i2i−2i2i-2200-22000000−2i2i000000000000000000002i−2i0000
χ372-2-2-2222-22-2-222-2-222-200002-200-2200000000002i2i−2i−2i002i−2i2i−2i00000000000000
χ382-2-2-2222-22-2-222-2-222-200002-200-220000000000−2i−2i2i2i00−2i2i−2i2i00000000000000
χ392-2-2-2222-22-2-222-2-222-20000-22002-200000000002i2i−2i−2i00−2i2i−2i2i00000000000000
χ402-2-2-2222-22-2-222-2-222-20000-22002-20000000000−2i−2i2i2i002i−2i2i−2i00000000000000
χ412-2-2-2222-2-222-2-222-22-22i−2i2i−2i000000000000−2i2i000000000000002-22i−2i00000000
χ422-2-2-2222-2-222-2-222-22-22i−2i2i−2i000000000000−2i2i00000000000000-22−2i2i00000000
χ432-2-2-2222-2-222-2-222-22-2−2i2i−2i2i0000000000002i−2i000000000000002-2−2i2i00000000
χ442-2-2-2222-2-222-2-222-22-2−2i2i−2i2i0000000000002i−2i00000000000000-222i−2i00000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-44-4-440-40-4040000000000000000000000022−2222−2200000000000000000000
χ47444-4-44-4-440-40-40400000000000000000000000−2222−222200000000000000000000
χ48444-4-44-4-4-404040-40000000004-4000000000000000000000000000000000000
χ49444-4-44-4-4-404040-4000000000-44000000000000000000000000000000000000
χ5044-444-4-4-4040-40-404004-4-440000000000000000000000000000000000000000
χ5144-444-4-4-4040-40-40400-444-40000000000000000000000000000000000000000
χ5244-444-4-4-40-404040-4000000000000000000000000000022−22−222200000000000000
χ5344-444-4-4-40-404040-40000000000000000000000000000−222222−2200000000000000
χ544-44-44-4-440-40-404040000000000000000000022−220000−2222000000000000000000
χ554-44-44-4-440-40-4040400000000000000000000−2222000022−22000000000000000000
χ564-4-44-44-444040-40-4000000000000000000000002i2−2i2−2i22i200000000000000000000
χ574-4-44-44-444040-40-400000000000000000000000−2i22i22i2−2i200000000000000000000
χ584-4-44-44-44-40-404040000000000000004-4000000000000000000000000000000
χ594-4-44-44-44-40-40404000000000000000-44000000000000000000000000000000
χ604-4-4-4444-4-4-444-4-444-4400000000000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-888-8-88-8000000000000000000000000000000000000000000000000000000

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