Finite Group Databasebeta

← Group #305721

Character table — Group #305721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-1-11-1-11111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1111111-1-1-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-11111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1111-1-111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-111-1
χ172222222222-2-22-22-20000-2-222222200-2-2-2-200-2-2000000000000200000000000000
χ182222222222-2-22-22-20000-2-22222-2-200222200-2-2000000000000-200000000000000
χ192222222222-2-22-22-20000-2-2-2-2-2-2220022-2-20022000000000000-200000000000000
χ202222222222-2-22-22-20000-2-2-2-2-2-2-2-200-2-2220022000000000000200000000000000
χ2122222222-2-222-22-222222-2-2000000-2-200002200-2-200002200000-20000000000000
χ2222222222-2-222-22-222222-2-2000000-2-20000-2-200220000-2-20000020000000000000
χ2322222222-2-222-22-22-2-2-2-2-2-20000002200002200220000-2-200000-20000000000000
χ2422222222-2-222-22-22-2-2-2-2-2-2000000220000-2-200-2-20000220000020000000000000
χ252-222-2-22-22222-2-2-2-222-2-22-200002-22-2002-2000000000000000000002-2000000000
χ262-222-2-22-22222-2-2-2-222-2-22-20000-222-200-2200000000000000000000-22000000000
χ272-222-2-22-22222-2-2-2-2-2-2222-200002-2-22002-200000000000000000000-22000000000
χ282-222-2-22-22222-2-2-2-2-2-2222-20000-22-2200-22000000000000000000002-2000000000
χ292-222-2-22-222-2-2-22-220000-2200002-20000-220000002i2i−2i−2i000000002i−2i00000000000
χ302-222-2-22-222-2-2-22-220000-2200002-20000-22000000−2i−2i2i2i00000000−2i2i00000000000
χ312-222-2-22-222-2-2-22-220000-220000-2200002-20000002i2i−2i−2i00000000−2i2i00000000000
χ322-222-2-22-222-2-2-22-220000-220000-2200002-2000000−2i−2i2i2i000000002i−2i00000000000
χ332-222-2-22-2-2-2222-22-222-2-2-22000000-22000000000000000000000000002i−2i002i−2i000
χ342-222-2-22-2-2-2222-22-222-2-2-22000000-2200000000000000000000000000−2i2i00−2i2i000
χ352-222-2-22-2-2-2222-22-2-2-222-220000002-2000000000000000000000000002i−2i00−2i2i000
χ362-222-2-22-2-2-2222-22-2-2-222-220000002-200000000000000000000000000−2i2i002i−2i000
χ372-2-2-2222-2002-2020-22-22-20022−2−2000000002i−2i2−2002−22−22i−2ii2i2−i2−i200000000i2−i200000
χ382-2-2-2222-2002-2020-22-22-20022−2−200000000−2i2i2−2002−22−2−2i2i−i2−i2i2i200000000−i2i200000
χ392-2-2-2222-2002-2020-22-22-200−2−222000000002i−2i−2200−22−222i−2i−i2−i2i2i200000000−i2i200000
χ402-2-2-2222-2002-2020-22-22-200−2−22200000000−2i2i−2200−22−22−2i2ii2i2−i2−i200000000i2−i200000
χ412-2-2-2222-2002-2020-2-22-220022−2−2000000002i−2i2−200−22−22−2i2i−i2−i2i2i200000000i2−i200000
χ422-2-2-2222-2002-2020-2-22-220022−2−200000000−2i2i2−200−22−222i−2ii2i2−i2−i200000000−i2i200000
χ432-2-2-2222-2002-2020-2-22-2200−2−222000000002i−2i−22002−22−2−2i2ii2i2−i2−i200000000−i2i200000
χ442-2-2-2222-2002-2020-2-22-2200−2−22200000000−2i2i−22002−22−22i−2i−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-40000000000000022−2222−2200000000000022−220000002-22-2000000000000000
χ47444-44-4-4-40000000000000022−2222−22000000000000−2222000000-22-22000000000000000
χ48444-44-4-4-400000000000000−2222−222200000000000022−22000000-22-22000000000000000
χ49444-44-4-4-400000000000000−2222−2222000000000000−22220000002-22-2000000000000000
χ5044-44-44-4-44-40040-40000000000000004-4000000000000000000000000000000000
χ5144-44-44-4-44-40040-4000000000000000-44000000000000000000000000000000000
χ5244-44-44-4-4-4400-404000000000000000000000000000000000000000000000002i2−2i20
χ5344-44-44-4-4-4400-40400000000000000000000000000000000000000000000000−2i22i20
χ5444-4-4-4-444004-40-4044-4-44000000000000000000000000000000000000000000000
χ5544-4-4-4-444004-40-404-444-4000000000000000000000000000000000000000000000
χ5644-4-4-4-44400-44040-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5744-4-4-4-44400-44040-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ584-444-4-44-4-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ594-4-444-4-444-400-40400000004-4-44000000000000000000000000000000000000000
χ604-4-444-4-444-400-4040000000-444-4000000000000000000000000000000000000000
χ614-4-444-4-44-440040-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ624-4-444-4-44-440040-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ634-4-4-4444-400-440-4040000002222−22−220000000000−2222000000000000000000000000000
χ644-4-4-4444-400-440-404000000−22−222222000000000022−22000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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