Finite Group Databasebeta

← Group #478413

Character table — Group #478413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111111111111122222222888888888888888888888888888816161616161616161616161616161616
order12222222222222224444444422444444444488888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ9111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ10111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-1
χ12111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-111
χ13111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1
χ14111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111
χ15111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ16111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ172222222222222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-2000000002-2002-2002-20022−2−222−2−222−2−222−2−20000000000000000
χ2222222222-2-2-2-2-2-2-2-2000000002-2002-2002-200−2−222−2−222−2−222−2−2220000000000000000
χ2322222222-2-2-2-2-2-2-2-2000000002-200-2200-220022−2−222−2−2−2−222−2−2220000000000000000
χ2422222222-2-2-2-2-2-2-2-2000000002-200-2200-2200−2−222−2−22222−2−222−2−20000000000000000
χ2522222222-2-2-2-2-2-2-2-200000000-22002-200-220022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222222-2-2-2-2-2-2-2-200000000-22002-200-2200−2−22222−2−2−2−22222−2−20000000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2200-22002-20022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2200-22002-200−2−22222−2−222−2−2−2−2220000000000000000
χ29222-2-2-22-22-222-2-2-22222-22-2-2-20000000000000000000000002i−2i2i−2i00002-200002i−2i0000
χ30222-2-2-22-22-222-2-2-22222-22-2-2-20000000000000000000000002i−2i2i−2i0000-220000−2i2i0000
χ31222-2-2-22-22-222-2-2-22222-22-2-2-2000000000000000000000000−2i2i−2i2i00002-20000−2i2i0000
χ32222-2-2-22-22-222-2-2-22222-22-2-2-2000000000000000000000000−2i2i−2i2i0000-2200002i−2i0000
χ3322-22-2-2-22-222-22-2-2222-22-22-2-200000000000000002i−2i2i−2i000000002i−2i00000000002-200
χ3422-22-2-2-22-222-22-2-2222-22-22-2-200000000000000002i−2i2i−2i00000000−2i2i0000000000-2200
χ3522-22-2-2-22-222-22-2-2222-22-22-2-20000000000000000−2i2i−2i2i000000002i−2i0000000000-2200
χ3622-22-2-2-22-222-22-2-2222-22-22-2-20000000000000000−2i2i−2i2i00000000−2i2i00000000002-200
χ372-22-22-2-22-22-22-22-222-222-2-22-20000000000002i−2i2i−2i000000000000002i−2i00000000002-2
χ382-22-22-2-22-22-22-22-222-222-2-22-20000000000002i−2i2i−2i00000000000000−2i2i0000000000-22
χ392-22-22-2-22-22-22-22-222-222-2-22-2000000000000−2i2i−2i2i000000000000002i−2i0000000000-22
χ402-22-22-2-22-22-22-22-222-222-2-22-2000000000000−2i2i−2i2i00000000000000−2i2i00000000002-2
χ412-2-222-22-22-2-2-222-22-2222-2-2-22000000000000000000002i−2i2i−2i00000000002-22i−2i000000
χ422-2-222-22-22-2-2-222-22-2222-2-2-22000000000000000000002i−2i2i−2i0000000000-22−2i2i000000
χ432-2-222-22-22-2-2-222-22-2222-2-2-2200000000000000000000−2i2i−2i2i00000000002-2−2i2i000000
χ442-2-222-22-22-2-2-222-22-2222-2-2-2200000000000000000000−2i2i−2i2i0000000000-222i−2i000000
χ45444-4-4-44-44-444-4-4-44-4-4-44-444400000000000000000000000000000000000000000000
χ46444-4-4-44-4-44-4-4444-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ47444-4-4-44-4-44-4-4444-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ4844-44-4-4-444-4-44-444-40000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ4944-44-4-4-444-4-44-444-4000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ5044-44-4-4-44-444-44-4-44-4-44-44-44400000000000000000000000000000000000000000000
χ5144-4-444-4-444-444-4-4-400000000004-40000000000000000000000000000000000000000
χ5244-4-444-4-444-444-4-4-40000000000-440000000000000000000000000000000000000000
χ5344-4-444-4-4-4-44-4-444444-4-4-4-44400000000000000000000000000000000000000000000
χ5444-4-444-4-4-4-44-4-4444-4-44444-4-400000000000000000000000000000000000000000000
χ554-444-44-4-4444-4-44-4-4000000000000004-4000000000000000000000000000000000000
χ564-444-44-4-4444-4-44-4-400000000000000-44000000000000000000000000000000000000
χ574-444-44-4-4-4-4-444-4444-44-4-44-4400000000000000000000000000000000000000000000
χ584-444-44-4-4-4-4-444-444-44-444-44-400000000000000000000000000000000000000000000
χ594-44-44-4-444-44-44-44-4000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ604-44-44-4-444-44-44-44-400000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ614-44-44-4-44-44-44-44-44-44-4-444-4400000000000000000000000000000000000000000000
χ624-4-444-44-44-4-4-444-444-4-4-4444-400000000000000000000000000000000000000000000
χ634-4-444-44-4-4444-4-44-400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ644-4-444-44-4-4444-4-44-40000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ654-4-4-4-444444-4-4-4-4444-4-444-4-4400000000000000000000000000000000000000000000
χ664-4-4-4-444444-4-4-4-444-444-4-444-400000000000000000000000000000000000000000000
χ674-4-4-4-4444-4-44444-4-40000000000000000004i−4i00000000000000000000000000000000
χ684-4-4-4-4444-4-44444-4-4000000000000000000−4i4i00000000000000000000000000000000

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