Finite Group Databasebeta

← Group #103722

Character table — Group #103722

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
χ9222222222222222-2-2-2-22-2-2-22-22-20000000000000000000000002200-2-200000000
χ10222222222222222-2-2-2-22-2-2-22-22-2000000000000000000000000-2-2002200000000
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
χ13222222222222-2-2-2-2-2-2-2-2-222-2-2-22000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ14222222222222-2-2-2-2-2-2-2-2-222-2-2-2200000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ1522222222-2-2-2-222222222-222-2-2-2-2000000000000000000000000002200-2-2000000
χ1622222222-2-2-2-222222222-222-2-2-2-200000000000000000000000000-2-20022000000
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
χ1922222222-2-2-2-2-2-2-22222-2-2-2-22-2220000000000000000000000000000000000002-2
χ2022222222-2-2-2-2-2-2-22222-2-2-2-22-222000000000000000000000000000000000000-22
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
χ23222-2-2-22-222-2-20002-22-20-200020000002i2i−2i−2i00000000i2i2−i2−i2i2i2−i2−i2000000002−22−200
χ24222-2-2-22-222-2-20002-22-20-200020000002i2i−2i−2i00000000−i2−i2i2i2−i2−i2i2i200000000−22−2200
χ25222-2-2-22-222-2-20002-22-20-20002000000−2i−2i2i2i00000000i2i2−i2−i2i2i2−i2−i200000000−22−2200
χ26222-2-2-22-222-2-20002-22-20-20002000000−2i−2i2i2i00000000−i2−i2i2i2−i2−i2i2i2000000002−22−200
χ27222-2-2-22-2-2-222000-22-220-20002002i2i−2i−2i000000000000i2i2−i2−i2−i2−i2i2i2000000002−2−2200
χ28222-2-2-22-2-2-222000-22-220-20002002i2i−2i−2i000000000000−i2−i2i2i2i2i2−i2−i200000000−222−200
χ29222-2-2-22-2-2-222000-22-220-2000200−2i−2i2i2i000000000000i2i2−i2−i2−i2−i2i2i200000000−222−200
χ30222-2-2-22-2-2-222000-22-220-2000200−2i−2i2i2i000000000000−i2−i2i2i2i2i2−i2−i2000000002−2−2200
χ3122-2-22-2-222-22-222-20000-2000-2020i2−i2i2−i2i2−i2i2−i222−2−222−2−2000000002i−2i000000000000
χ3222-2-22-2-222-22-222-20000-2000-2020i2−i2i2−i2i2−i2i2−i2−2−222−2−22200000000−2i2i000000000000
χ3322-2-22-2-222-22-222-20000-2000-2020−i2i2−i2i2−i2i2−i2i222−2−222−2−200000000−2i2i000000000000
χ3422-2-22-2-222-22-222-20000-2000-2020−i2i2−i2i2−i2i2−i2i2−2−222−2−222000000002i−2i000000000000
χ3522-2-22-2-222-22-2-2-220000200020-20i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000002-200000000
χ3622-2-22-2-222-22-2-2-220000200020-20i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2000000000000-2200000000
χ3722-2-22-2-222-22-2-2-220000200020-20−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2000000000000-2200000000
χ3822-2-22-2-222-22-2-2-220000200020-20−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000002-200000000
χ392-2-222-22-200002-22-2-222-202-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2002-20000000000
χ402-2-222-22-200002-22-2-222-202-2000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200-220000000000
χ412-2-222-22-200002-22-2-222-202-2000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200-220000000000
χ422-2-222-22-200002-22-2-222-202-2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2002-20000000000
χ432-2-222-22-20000-22-222-2-2202-20000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000002i−2i000000
χ442-2-222-22-20000-22-222-2-2202-20000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000−2i2i000000
χ452-2-222-22-20000-22-222-2-2202-2000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000−2i2i000000
χ462-2-222-22-20000-22-222-2-2202-2000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000002i−2i000000
χ47444-4-4-44-444-4-4000-44-4404000-40000000000000000000000000000000000000000
χ48444-4-4-44-4-4-4440004-44-404000-40000000000000000000000000000000000000000
χ4944-44-44-4-44-4-44000000000000000000022−22−2222000000000000000000000000000000
χ5044-44-44-4-44-4-440000000000000000000−222222−22000000000000000000000000000000
χ5144-44-44-4-4-444-400000000000000022−22−22220000000000000000000000000000000000
χ5244-44-44-4-4-444-4000000000000000−222222−220000000000000000000000000000000000
χ5344-4-44-4-44-44-4444-40000-400040-4000000000000000000000000000000000000000
χ5444-4-44-4-44-44-44-4-4400004000-404000000000000000000000000000000000000000
χ554-44-444-4-400004-4-4000040000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ564-44-444-4-400004-4-400004000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ574-44-444-4-40000-4440000-40000000000000002-2-22-222-20000000000000000000000
χ584-44-444-4-40000-4440000-4000000000000000-222-22-2-220000000000000000000000
χ594-4-444-44-400004-4444-4-4-40-44000000000000000000000000000000000000000000
χ604-4-444-44-40000-44-4-4-44440-44000000000000000000000000000000000000000000
χ614-4-4-4-444400000004-4-440000000000000000000000002-2-22-222-200000000000000
χ624-4-4-4-444400000004-4-44000000000000000000000000-222-22-2-2200000000000000
χ634-4-4-4-44440000000-444-40000000000000000000000002-2-222-2-2200000000000000
χ644-4-4-4-44440000000-444-4000000000000000000000000-222-2-222-200000000000000
χ658-888-8-8-88000000000000000000000000000000000000000000000000000000000

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