Finite Group Databasebeta

← Group #103756

Character table — Group #103756

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ9222222222222222-2-2-2-22-22-2-2-22-200000000000000000000000022-2-20000000000
χ10222222222222222-2-2-2-22-22-2-2-22-2000000000000000000000000-2-2220000000000
χ11222222222222-2-2-22222-22-2-2-22-2-22222-2-2-2-2000000000000000000000000000000
χ12222222222222-2-2-22222-22-2-2-22-2-2-2-2-2-22222000000000000000000000000000000
χ13222222222222-2-2-2-2-2-2-2-2-2-222-2-22000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ14222222222222-2-2-2-2-2-2-2-2-2-222-2-2200000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ1522222222-2-2-2-222222222-2-222-2-2-2000000000000000000000000000022-2-2000000
χ1622222222-2-2-2-222222222-2-222-2-2-20000000000000000000000000000-2-222000000
χ1722222222-2-2-2-2222-2-2-2-222-2-2-22-220000000000000000000000000000000022-2-200
χ1822222222-2-2-2-2222-2-2-2-222-2-2-22-2200000000000000000000000000000000-2-22200
χ1922222222-2-2-2-2-2-2-22222-2-22-2-2-2220000000000000000000000000000000000002-2
χ2022222222-2-2-2-2-2-2-22222-2-22-2-2-222000000000000000000000000000000000000-22
χ2122222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000000000002222-2-2-2-200000000000000
χ2222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000000000000-2-2-2-2222200000000000000
χ232222-2-2-2-222-2-20002-22-202000-200000022-2-20000000022−2−222−2−2000000002−22−200
χ242222-2-2-2-222-2-20002-22-202000-200000022-2-200000000−2−222−2−22200000000−22−2200
χ252222-2-2-2-222-2-20002-22-202000-2000000-2-2220000000022−2−222−2−200000000−22−2200
χ262222-2-2-2-222-2-20002-22-202000-2000000-2-22200000000−2−222−2−222000000002−22−200
χ272222-2-2-2-2-2-222000-22-2202000-20022-2-200000000000022−2−2−2−222000000002−2−2200
χ282222-2-2-2-2-2-222000-22-2202000-20022-2-2000000000000−2−22222−2−200000000−222−200
χ292222-2-2-2-2-2-222000-22-2202000-200-2-22200000000000022−2−2−2−22200000000−222−200
χ302222-2-2-2-2-2-222000-22-2202000-200-2-222000000000000−2−22222−2−2000000002−2−2200
χ3122-2-222-2-22-22-222-20000-202000-202−22−22−22−222−2−222−2−2000000002-2000000000000
χ3222-2-222-2-22-22-222-20000-202000-202−22−22−22−2−2−222−2−22200000000-22000000000000
χ3322-2-222-2-22-22-222-20000-202000-20−22−22−22−2222−2−222−2−200000000-22000000000000
χ3422-2-222-2-22-22-222-20000-202000-20−22−22−22−22−2−222−2−222000000002-2000000000000
χ3522-2-222-2-22-22-2-2-22000020-2000202−22−2−22−22i2i2−i2−i2−i2−i2i2i200000000002i−2i0000000000
χ3622-2-222-2-22-22-2-2-22000020-2000202−22−2−22−22−i2−i2i2i2i2i2−i2−i20000000000−2i2i0000000000
χ3722-2-222-2-22-22-2-2-22000020-200020−22−222−22−2i2i2−i2−i2−i2−i2i2i20000000000−2i2i0000000000
χ3822-2-222-2-22-22-2-2-22000020-200020−22−222−22−2−i2−i2i2i2i2i2−i2−i200000000002i−2i0000000000
χ392-22-22-2-2200002-22-2-222-2002-200000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000002-2000000
χ402-22-22-2-2200002-22-2-222-2002-200000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000-22000000
χ412-22-22-2-2200002-22-2-222-2002-200000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000-22000000
χ422-22-22-2-2200002-22-2-222-2002-200000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002-2000000
χ432-22-22-2-220000-22-222-2-22002-2000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200002i−2i00000000
χ442-22-22-2-220000-22-222-2-22002-2000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000−2i2i00000000
χ452-22-22-2-220000-22-222-2-22002-200000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i20000−2i2i00000000
χ462-22-22-2-220000-22-222-2-22002-200000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i200002i−2i00000000
χ474444-4-4-4-444-4-4000-44-440-400040000000000000000000000000000000000000000
χ484444-4-4-4-4-4-4440004-44-40-400040000000000000000000000000000000000000000
χ4944-4-444-4-4-44-4444-40000-40-40004000000000000000000000000000000000000000
χ5044-4-444-4-4-44-44-4-440000404000-4000000000000000000000000000000000000000
χ5144-4-4-4-4444-4-44000000000000000000022−22−2222000000000000000000000000000000
χ5244-4-4-4-4444-4-440000000000000000000−222222−22000000000000000000000000000000
χ5344-4-4-4-444-444-400000000000000022−22−22220000000000000000000000000000000000
χ5444-4-4-4-444-444-4000000000000000−222222−220000000000000000000000000000000000
χ554-44-44-4-4400004-4444-4-4-400-4400000000000000000000000000000000000000000
χ564-44-44-4-440000-44-4-4-444400-4400000000000000000000000000000000000000000
χ574-44-4-444-400000004-4-440000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ584-44-4-444-400000004-4-44000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ594-44-4-444-40000000-444-40000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ604-44-4-444-40000000-444-4000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ614-4-444-44-400004-4-4000040000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ624-4-444-44-400004-4-400004000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ634-4-444-44-40000-4440000-40000000000000002-2-22-222-20000000000000000000000
χ644-4-444-44-40000-4440000-4000000000000000-222-22-2-220000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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