Finite Group Databasebeta

← Group #345101

Character table — Group #345101

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-11-11-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-11-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1111-1-111-1-1-1-1-1-1-11
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1111-1-111-1-111-1-1-1-11-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-11111-1-111111-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1-1-1111111-11
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-1-111111111-1-1-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-111-1-111-1-1-1-1-1-111-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-111-1-1-1-1-111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-11-1-1-1-1-1-11111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111111111-1-111-1-1-1-1
χ172222222222-2-2-2-222-2-2000000002222-2-2-2-20000000000220022-20-2000000000000000
χ182222222222-2-2-2-222-2-2000000002222-2-2-2-20000000000-2-200-2-2202000000000000000
χ192222222222-2-2-2-222-2-200000000-2-2-2-2222200000000002200-2-2-202000000000000000
χ202222222222-2-2-2-222-2-200000000-2-2-2-222220000000000-2-2002220-2000000000000000
χ2122222222-2-22222-2-2-2-22222-2-2-2-20000000000000000220022000-20-200000000000000
χ2222222222-2-22222-2-2-2-22222-2-2-2-20000000000000000-2-200-2-200020200000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2222200000000000000002200-2-2000-20200000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-222220000000000000000-2-2002200020-200000000000000
χ25222-2-2-2-222-200002-200i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00002222−2−2−2−2002i−2i002-2000000002−2i2−i2000000
χ26222-2-2-2-222-200002-200i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00002222−2−2−2−200−2i2i00-2200000000−22−i2i2000000
χ27222-2-2-2-222-200002-200i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i0000−2−2−2−22222002i−2i00-22000000002−2−i2i2000000
χ28222-2-2-2-222-200002-200i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i0000−2−2−2−2222200−2i2i002-200000000−22i2−i2000000
χ29222-2-2-2-222-200002-200−i2−i2i2i2−i2−i2i2i22i2i−2i−2i0000−2−2−2−22222002i−2i002-200000000−22−i2i2000000
χ30222-2-2-2-222-200002-200−i2−i2i2i2−i2−i2i2i22i2i−2i−2i0000−2−2−2−2222200−2i2i00-22000000002−2i2−i2000000
χ31222-2-2-2-222-200002-200−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00002222−2−2−2−2002i−2i00-2200000000−22i2−i2000000
χ32222-2-2-2-222-200002-200−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00002222−2−2−2−200−2i2i002-2000000002−2−i2i2000000
χ3322-22-22-2-2002-22-200002-22-20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22i−2i002i−2i000000000000002−22−200
χ3422-22-22-2-2002-22-200002-22-20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i00−2i2i00000000000000−22−2200
χ3522-22-22-2-2002-22-200002-22-20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i−2i002i−2i00000000000000−22−2200
χ3622-22-22-2-2002-22-200002-22-20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2i2i00−2i2i000000000000002−22−200
χ3722-22-22-2-2002-22-20000-22-220000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i00−2i2i000000000000002−2−2200
χ3822-22-22-2-2002-22-20000-22-220000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i002i−2i00000000000000−222−200
χ3922-22-22-2-2002-22-20000-22-220000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i00−2i2i00000000000000−222−200
χ4022-22-22-2-2002-22-20000-22-220000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i002i−2i000000000000002−2−2200
χ412-2-222-2-2222-2-222-2-2-2200000000000000002-22-22-22-20000000000002i−2i2i−2i0000000000
χ422-2-222-2-2222-2-222-2-2-2200000000000000002-22-22-22-2000000000000−2i2i−2i2i0000000000
χ432-2-222-2-2222-2-222-2-2-220000000000000000-22-22-22-220000000000002i−2i−2i2i0000000000
χ442-2-222-2-2222-2-222-2-2-220000000000000000-22-22-22-22000000000000−2i2i2i−2i0000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-44-440000-44002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ47444-4-4-4-44-440000-4400−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ4844-44-44-4-400-44-440000000000002i2−2i22i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ4944-44-44-4-400-44-44000000000000−2i22i2−2i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ5044-4-44-44-400000000002i2−2i2−2i22i2000022−22−22220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ5144-4-44-44-400000000002i2−2i2−2i22i20000−222222−2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ5244-4-44-44-40000000000−2i22i22i2−2i2000022−22−222200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ5344-4-44-44-40000000000−2i22i22i2−2i20000−222222−220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ544-444-4-44-4004-4-44000000004i−4i4i−4i000000000000000000000000000000000000000000
χ554-444-4-44-4004-4-4400000000−4i4i−4i4i000000000000000000000000000000000000000000
χ564-444-4-44-400-444-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ574-444-4-44-400-444-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ584-44-444-4-40000000000000022−22−222200002i2−2i22i2−2i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ594-44-444-4-40000000000000022−22−22220000−2i22i2−2i22i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ604-44-444-4-400000000000000−222222−2200002i2−2i22i2−2i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ614-44-444-4-400000000000000−222222−220000−2i22i2−2i22i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ624-4-444-4-444444-4-4-4-44-400000000000000000000000000000000000000000000000000
χ634-4-444-4-44-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ644-4-444-4-44-4-4-4-444444-400000000000000000000000000000000000000000000000000
χ654-4-4-4-44444-40000-4400000000000000000022−2222−22−2222−222200000000000000000000000000
χ664-4-4-4-44444-40000-44000000000000000000−2222−222222−2222−2200000000000000000000000000
χ674-4-4-4-4444-4400004-4000000000000004-4-440000000000000000000000000000000000
χ684-4-4-4-4444-4400004-400000000000000-444-40000000000000000000000000000000000

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