Finite Group Databasebeta

← Group #103724

Character table — Group #103724

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-111-1-1-1-1-1-1
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
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111
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
χ9222222222222222-2-2-2-22-22-2-2-22-20000000000000000000000002200-2-200000000
χ10222222222222222-2-2-2-22-22-2-2-22-2000000000000000000000000-2-2002200000000
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
χ1522222222-2-2-2-222222222-2-222-2-2-2000000000000000000000000002200-2-2000000
χ1622222222-2-2-2-222222222-2-222-2-2-200000000000000000000000000-2-20022000000
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
χ23222-22-2-2-222-2-222-20000-202000-2022−2−222−2−222−2−222−2−2000000002-2000000000000
χ24222-22-2-2-222-2-222-20000-202000-2022−2−222−2−2−2−222−2−22200000000-22000000000000
χ25222-22-2-2-222-2-222-20000-202000-20−2−222−2−22222−2−222−2−200000000-22000000000000
χ26222-22-2-2-222-2-222-20000-202000-20−2−222−2−222−2−222−2−222000000002-2000000000000
χ27222-22-2-2-222-2-2-2-22000020-20002022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000002i−2i00000000
χ28222-22-2-2-222-2-2-2-22000020-20002022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000−2i2i00000000
χ29222-22-2-2-222-2-2-2-22000020-200020−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000−2i2i00000000
χ30222-22-2-2-222-2-2-2-22000020-200020−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000002i−2i00000000
χ3122-22-2-22-22-22-20002-22-20-200020000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i2000000002−22−200
χ3222-22-2-22-22-22-20002-22-20-200020000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i200000000−22−2200
χ3322-22-2-22-22-22-20002-22-20-20002000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i200000000−22−2200
χ3422-22-2-22-22-22-20002-22-20-20002000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i2000000002−22−200
χ3522-22-2-22-2-22-22000-22-220-20002002i−2i2i−2i000000000000i2i2−i2−i2−i2−i2i2i2000000002−2−2200
χ3622-22-2-22-2-22-22000-22-220-20002002i−2i2i−2i000000000000−i2−i2i2i2i2i2−i2−i200000000−222−200
χ3722-22-2-22-2-22-22000-22-220-2000200−2i2i−2i2i000000000000i2i2−i2−i2−i2−i2i2i200000000−222−200
χ3822-22-2-22-2-22-22000-22-220-2000200−2i2i−2i2i000000000000−i2−i2i2i2i2i2−i2−i2000000002−2−2200
χ392-22-2-222-200002-22-2-222-2002-200000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2002-20000000000
χ402-22-2-222-200002-22-2-222-2002-200000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200-220000000000
χ412-22-2-222-200002-22-2-222-2002-200000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200-220000000000
χ422-22-2-222-200002-22-2-222-2002-200000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2002-20000000000
χ432-22-2-222-20000-22-222-2-22002-2000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000002i−2i000000
χ442-22-2-222-20000-22-222-2-22002-2000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000−2i2i000000
χ452-22-2-222-20000-22-222-2-22002-200000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000−2i2i000000
χ462-22-2-222-20000-22-222-2-22002-200000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000002i−2i000000
χ47444-44-4-4-4-4-44444-40000-40-40004000000000000000000000000000000000000000
χ48444-44-4-4-4-4-444-4-440000404000-4000000000000000000000000000000000000000
χ4944-44-4-44-44-44-4000-44-4404000-40000000000000000000000000000000000000000
χ5044-44-4-44-4-44-440004-44-404000-40000000000000000000000000000000000000000
χ5144-4-4-44-444-4-4400000000000000000002i2−2i2−2i22i2000000000000000000000000000000
χ5244-4-4-44-444-4-440000000000000000000−2i22i22i2−2i2000000000000000000000000000000
χ5344-4-4-44-44-444-40000000000000002i2−2i2−2i22i20000000000000000000000000000000000
χ5444-4-4-44-44-444-4000000000000000−2i22i22i2−2i20000000000000000000000000000000000
χ554-444-4-4-4400004-4-4000040000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ564-444-4-4-4400004-4-400004000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ574-444-4-4-440000-4440000-40000000000000002-2-22-222-20000000000000000000000
χ584-444-4-4-440000-4440000-4000000000000000-222-22-2-220000000000000000000000
χ594-44-4-444-400004-4444-4-4-400-4400000000000000000000000000000000000000000
χ604-44-4-444-40000-44-4-4-444400-4400000000000000000000000000000000000000000
χ614-4-4-44-44400000004-4-440000000000000000000000002-2-22-222-200000000000000
χ624-4-4-44-44400000004-4-44000000000000000000000000-222-22-2-2200000000000000
χ634-4-4-44-4440000000-444-40000000000000000000000002-2-222-2-2200000000000000
χ644-4-4-44-4440000000-444-4000000000000000000000000-222-2-222-200000000000000
χ658-8-8888-8-8000000000000000000000000000000000000000000000000000000000

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