Finite Group Databasebeta

← Group #336753

Character table — Group #336753

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888824448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-111-1-1-1-11111111111-1-1-11-1-111-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1111111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-111-1-11
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
χ9111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-11-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111-11
χ11111111111111111111-1-1-1-11111-1-11111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-11-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-111-111-1-1-11-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1111-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111111111111-1-1-1-11-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-111-111
χ172222222222-2-2-2-222-2-20000222200220000-2-2-2-2000000-2-20000000020000000000
χ182222222222-2-2-2-222-2-20000222200-2-200002222000000-2-200000000-20000000000
χ192222222222-2-2-2-222-2-20000-2-2-2-20022000022-2-20000002200000000-20000000000
χ202222222222-2-2-2-222-2-20000-2-2-2-200-2-20000-2-222000000220000000020000000000
χ2122222222-2-22222-2-2-2-222220000220022-2-20000-2-200000000000000000-20000000
χ2222222222-2-22222-2-2-2-222220000-2-200-2-2220000-2-20000000000000000020000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200002200-2-22200002200000000000000000-20000000
χ2422222222-2-22222-2-2-2-2-2-2-2-20000-2-20022-2-20000220000000000000000020000000
χ25222-2-2-2-222-200002-200i2i2−i2−i22i2i−2i−2i000000002i−2i2-2i2−i2i2i2−i2−i200000022−2−200002−200000
χ26222-2-2-2-222-200002-200i2i2−i2−i22i2i−2i−2i00000000−2i2i-22i2−i2−i2−i2i2i200000022−2−20000−2200000
χ27222-2-2-2-222-200002-200i2i2−i2−i2−2i−2i2i2i000000002i−2i-22i2−i2−i2−i2i2i2000000−2−22200002−200000
χ28222-2-2-2-222-200002-200i2i2−i2−i2−2i−2i2i2i00000000−2i2i2-2i2−i2i2i2−i2−i2000000−2−2220000−2200000
χ29222-2-2-2-222-200002-200−i2−i2i2i22i2i−2i−2i000000002i−2i2-2−i2i2−i2−i2i2i2000000−2−2220000−2200000
χ30222-2-2-2-222-200002-200−i2−i2i2i22i2i−2i−2i00000000−2i2i-22−i2i2i2i2−i2−i2000000−2−22200002−200000
χ31222-2-2-2-222-200002-200−i2−i2i2i2−2i−2i2i2i000000002i−2i-22−i2i2i2i2−i2−i200000022−2−20000−2200000
χ32222-2-2-2-222-200002-200−i2−i2i2i2−2i−2i2i2i00000000−2i2i2-2−i2i2−i2−i2i2i200000022−2−200002−200000
χ3322-2-22-22-2-2-222-2-2222-200000000000000000000002i−2i2i−2i0022-2-2000002i−2i00000000
χ3422-2-22-22-2-2-222-2-2222-200000000000000000000002i−2i2i−2i00-2-22200000−2i2i00000000
χ3522-2-22-22-2-2-222-2-2222-20000000000000000000000−2i2i−2i2i0022-2-200000−2i2i00000000
χ3622-2-22-22-2-2-222-2-2222-20000000000000000000000−2i2i−2i2i00-2-222000002i−2i00000000
χ372-22-2-222-2002-22-200002i−2i2i−2ii2−i2i2−i22-2002i−2i000000000000i2−i22−22−22−22−2000000i2−i2000
χ382-22-2-222-2002-22-200002i−2i2i−2ii2−i2i2−i2-2200−2i2i000000000000i2−i2−22−222−22−2000000−i2i2000
χ392-22-2-222-2002-22-200002i−2i2i−2i−i2i2−i2i22-2002i−2i000000000000−i2i2−22−22−22−22000000−i2i2000
χ402-22-2-222-2002-22-200002i−2i2i−2i−i2i2−i2i2-2200−2i2i000000000000−i2i22−22−2−22−22000000i2−i2000
χ412-22-2-222-2002-22-20000−2i2i−2i2ii2−i2i2−i22-200−2i2i000000000000i2−i2−22−22−22−22000000i2−i2000
χ422-22-2-222-2002-22-20000−2i2i−2i2ii2−i2i2−i2-22002i−2i000000000000i2−i22−22−2−22−22000000−i2i2000
χ432-22-2-222-2002-22-20000−2i2i−2i2i−i2i2−i2i22-200−2i2i000000000000−i2i22−22−22−22−2000000−i2i2000
χ442-22-2-222-2002-22-20000−2i2i−2i2i−i2i2−i2i2-22002i−2i000000000000−i2i2−22−222−22−2000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-4-44-440000-44002i22i2−2i2−2i20000000000000000−2i22i20000000000000000000000000
χ47444-4-4-4-44-440000-4400−2i2−2i22i22i200000000000000002i2−2i20000000000000000000000000
χ4844-44-44-4-44-40000-440000000000004-400000000000000000000000000000000000
χ4944-44-44-4-44-40000-44000000000000-4400000000000000000000000000000000000
χ5044-44-44-4-4-4400004-400000000000000000000000022−22−2222000000000000000000000
χ5144-44-44-4-4-4400004-4000000000000000000000000−222222−22000000000000000000000
χ5244-4-44-44-44444-4-4-4-4-4400000000000000000000000000000000000000000000000
χ5344-4-44-44-444-4-444-4-44-400000000000000000000000000000000000000000000000
χ5444-4-44-44-4-4-4-4-44444-4400000000000000000000000000000000000000000000000
χ554-4444-4-4-4000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ564-4444-4-4-4000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ574-4444-4-4-40000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ584-4444-4-4-40000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ594-44-4-444-400-44-44000000002i2−2i22i2−2i2000000000000000000−2i22i20000000000000000000
χ604-44-4-444-400-44-4400000000−2i22i2−2i22i20000000000000000002i2−2i20000000000000000000
χ614-4-44-4-444004-4-440000000000000000000000000000000022−22−2222000000000000000
χ624-4-44-4-444004-4-4400000000000000000000000000000000−222222−22000000000000000
χ634-4-44-4-44400-444-40000000000000000004-40000000000000000000000000000000
χ644-4-44-4-44400-444-4000000000000000000-440000000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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