Finite Group Databasebeta

← Group #288299

Character table — Group #288299

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888844444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-11-111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-111-1-1-1-1-11-1-111-1-1-1-111-11
χ11111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1111-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-11-1-111-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1111-1
χ172222222222-22-2-2-22-2-200002222-2-20000-2-200220000-2-2000000000000000000
χ182222222222-22-2-2-22-2-2000022-2-2220000-2-200-2-2000022000000000000000000
χ192222222222-22-2-2-22-2-20000-2-222-2-200002200-2-2000022000000000000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-22200002200220000-2-2000000000000000000
χ2122222222-2-22-2222-2-2-22222000000222200-2-2000000000000-2-2000000000000
χ2222222222-2-22-2222-2-2-22222000000-2-2-2-200-2-200000000000022000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-200000022-2-20022000000000000-22000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2000000-2-22200220000000000002-2000000000000
χ25222-2-2-2-22222-2-22-2-2-220000002i−2i2i−2i00000000002i2i−2i−2i0022-2-200000000000000
χ26222-2-2-2-22222-2-22-2-2-220000002i−2i2i−2i0000000000−2i−2i2i2i00-2-22200000000000000
χ27222-2-2-2-22222-2-22-2-2-22000000−2i2i−2i2i00000000002i2i−2i−2i00-2-22200000000000000
χ28222-2-2-2-22222-2-22-2-2-22000000−2i2i−2i2i0000000000−2i−2i2i2i0022-2-200000000000000
χ29222-2-2-2-2222-2-22-22-22-222-2-2002i−2i−2i2i0000002-20000000000000000002i−2i000000
χ30222-2-2-2-2222-2-22-22-22-222-2-200−2i2i2i−2i0000002-2000000000000000000−2i2i000000
χ31222-2-2-2-2222-2-22-22-22-2-2-222002i−2i−2i2i000000-22000000000000000000−2i2i000000
χ32222-2-2-2-2222-2-22-22-22-2-2-22200−2i2i2i−2i000000-220000000000000000002i−2i000000
χ33222-2-2-2-22-2-2-222-222-2222-2-2000000000000-22000000000000002-22-200000000
χ34222-2-2-2-22-2-2-222-222-2222-2-2000000000000-2200000000000000-22-2200000000
χ35222-2-2-2-22-2-2-222-222-22-2-2220000000000002-2000000000000002-2-2200000000
χ36222-2-2-2-22-2-2-222-222-22-2-2220000000000002-200000000000000-222-200000000
χ372-2-2-2-222200-20-2220002-22-20000002-22-200002−200002−22−22−2000000002−22−200
χ382-2-2-2-222200-20-2220002-22-20000002-22-20000−220000−22−22−2200000000−22−2200
χ392-2-2-2-222200-20-2220002-22-2000000-22-2200002−200002−22−22−200000000−22−2200
χ402-2-2-2-222200-20-2220002-22-2000000-22-220000−220000−22−22−22000000002−22−200
χ412-2-2-2-222200-20-222000-22-220000002-2-2200002−200002−2−22−22000000002−2−2200
χ422-2-2-2-222200-20-222000-22-220000002-2-220000−220000−222−22−200000000−222−200
χ432-2-2-2-222200-20-222000-22-22000000-222-200002−200002−2−22−2200000000−222−200
χ442-2-2-2-222200-20-222000-22-22000000-222-20000−220000−222−22−2000000002−2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-4-44-4-444-44-444-400000000000000000000000000000000000000000000
χ4744-44-44-4-44-404000-4000000000000000000000022−2222−2200000000000000000000
χ4844-44-44-4-44-404000-40000000000000000000000−2222−222200000000000000000000
χ4944-44-44-4-4-440-4000400000000000000004i−4i0000000000000000000000000000
χ5044-44-44-4-4-440-400040000000000000000−4i4i0000000000000000000000000000
χ5144-4-44-44-44-40-4000400000000000000000000002i2−2i2−2i22i200000000000000000000
χ5244-4-44-44-44-40-400040000000000000000000000−2i22i22i2−2i200000000000000000000
χ5344-4-44-44-4-4404000-40000004-400000000000000000000000000000000000000
χ5444-4-44-44-4-4404000-4000000-4400000000000000000000000000000000000000
χ554-4-444-4-440040-4-440004-4-440000000000000000000000000000000000000000
χ564-4-444-4-440040-4-44000-444-40000000000000000000000000000000000000000
χ574-4-444-4-4400-4044-40000000000000000000000000000022−22−222200000000000000
χ584-4-444-4-4400-4044-400000000000000000000000000000−222222−2200000000000000
χ594-4-4-4-444400404-4-400000000000000000000022−220000−2222000000000000000000
χ604-4-4-4-444400404-4-4000000000000000000000−2222000022−22000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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