Finite Group Databasebeta

← Group #336749

Character table — Group #336749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888824448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1-1-111-1-1-1-11111111111-11-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1111111-1
χ9111111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-1
χ11111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-1-1
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-111
χ13111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-111-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111111111-1-1-1-1-11-1
χ1722222222222-2-2-2-22-2-20000222200002200-2-2-2-2000000-2-20000000020000000000
χ1822222222222-2-2-2-22-2-2000022220000-2-2002222000000-2-200000000-20000000000
χ1922222222222-2-2-2-22-2-20000-2-2-2-20000220022-2-20000002200000000-20000000000
χ2022222222222-2-2-2-22-2-20000-2-2-2-20000-2-200-2-222000000220000000020000000000
χ2122222222-2-2-22222-2-2-222220000222200-2-20000-2-2000000000000000-2000000000
χ2222222222-2-2-22222-2-2-222220000-2-2-2-200220000-2-20000000000000002000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2000022-2-200-2-20000220000000000000002000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-20000-2-2220022000022000000000000000-2000000000
χ25222-2-2-2-222-2-2000020022−2−22i2i−2i−2i000000002i−2i2-22−222−2−2000000i2i2−i2−i20000i2−i200000
χ26222-2-2-2-222-2-2000020022−2−22i2i−2i−2i00000000−2i2i-222−2−2−222000000i2i2−i2−i20000−i2i200000
χ27222-2-2-2-222-2-2000020022−2−2−2i−2i2i2i000000002i−2i-222−2−2−222000000−i2−i2i2i20000i2−i200000
χ28222-2-2-2-222-2-2000020022−2−2−2i−2i2i2i00000000−2i2i2-22−222−2−2000000−i2−i2i2i20000−i2i200000
χ29222-2-2-2-222-2-20000200−2−2222i2i−2i−2i000000002i−2i2-2−22−2−222000000−i2−i2i2i20000−i2i200000
χ30222-2-2-2-222-2-20000200−2−2222i2i−2i−2i00000000−2i2i-22−2222−2−2000000−i2−i2i2i20000i2−i200000
χ31222-2-2-2-222-2-20000200−2−222−2i−2i2i2i000000002i−2i-22−2222−2−2000000i2i2−i2−i20000−i2i200000
χ32222-2-2-2-222-2-20000200−2−222−2i−2i2i2i00000000−2i2i2-2−22−2−222000000i2i2−i2−i20000i2−i200000
χ3322-2-2-222-20002-22-20002-22-2i2−i2i2−i22i−2i2i−2i00000000000000i2−i222−2−2i2−i2i2−i20000002−2000
χ3422-2-2-222-20002-22-20002-22-2i2−i2i2−i2−2i2i−2i2i00000000000000i2−i2−2−222i2−i2i2−i2000000−22000
χ3522-2-2-222-20002-22-20002-22-2−i2i2−i2i22i−2i2i−2i00000000000000−i2i2−2−222−i2i2−i2i2000000−22000
χ3622-2-2-222-20002-22-20002-22-2−i2i2−i2i2−2i2i−2i2i00000000000000−i2i222−2−2−i2i2−i2i20000002−2000
χ3722-2-2-222-20002-22-2000-22-22i2−i2i2−i22i−2i−2i2i00000000000000i2−i222−2−2−i2i2−i2i2000000−22000
χ3822-2-2-222-20002-22-2000-22-22i2−i2i2−i2−2i2i2i−2i00000000000000i2−i2−2−222−i2i2−i2i20000002−2000
χ3922-2-2-222-20002-22-2000-22-22−i2i2−i2i22i−2i−2i2i00000000000000−i2i2−2−222i2−i2i2−i20000002−2000
χ4022-2-2-222-20002-22-2000-22-22−i2i2−i2i2−2i2i2i−2i00000000000000−i2i222−2−2i2−i2i2−i2000000−22000
χ412-222-2-22-2-2-2222-2-222-200000000000000000000002i−2i2i−2i002-22-20000002i−2i0000000
χ422-222-2-22-2-2-2222-2-222-200000000000000000000002i−2i2i−2i00-22-22000000−2i2i0000000
χ432-222-2-22-2-2-2222-2-222-20000000000000000000000−2i2i−2i2i002-22-2000000−2i2i0000000
χ442-222-2-22-2-2-2222-2-222-20000000000000000000000−2i2i−2i2i00-22-220000002i−2i0000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-4-44-4440000-4002222−22−220000000000000000−22220000000000000000000000000
χ47444-4-4-4-44-4440000-400−22−222222000000000000000022−220000000000000000000000000
χ4844-444-4-4-4000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ4944-444-4-4-4000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ5044-444-4-4-40000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ5144-444-4-4-40000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ5244-4-4-444-4000-44-4400000002i2−2i22i2−2i2000000000000000000−2i22i20000000000000000000
χ5344-4-4-444-4000-44-440000000−2i22i2−2i22i20000000000000000002i2−2i20000000000000000000
χ544-444-4-44-444-444-4-4-4-4400000000000000000000000000000000000000000000000
χ554-444-4-44-444-4-4-444-44-400000000000000000000000000000000000000000000000
χ564-444-4-44-4-4-44-4-4444-4400000000000000000000000000000000000000000000000
χ574-44-444-4-44-440000-4000000000000004-4000000000000000000000000000000000
χ584-44-444-4-44-440000-400000000000000-44000000000000000000000000000000000
χ594-44-444-4-4-44-4000040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ604-44-444-4-4-44-400004000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ614-4-4-44-4440004-4-44000000000000000000000000000000022−22−2222000000000000000
χ624-4-4-44-4440004-4-440000000000000000000000000000000−222222−22000000000000000
χ634-4-4-44-444000-444-4000000000000000004-40000000000000000000000000000000
χ644-4-4-44-444000-444-400000000000000000-440000000000000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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