Finite Group Databasebeta

← Group #138363

Character table — Group #138363

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222244444444888888888816161616161616161616161616161616161616163232
order12222244442244444444444444448888888888888888888844
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ91111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i1-1
χ101111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii1-1
χ111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii-11
χ121111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i-11
χ131111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii-11
χ141111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i-11
χ151111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i1-1
χ161111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii1-1
χ172222222222222-2-2-2-22-2-22222-2-2-2-20000000000000000000000
χ182222222222222-2-2-2-22-2-2-2-2-2-222220000000000000000000000
χ192222222222-2-2-22222-2-2-222-2-2-2-2220000000000000000000000
χ202222222222-2-2-22222-2-2-2-2-22222-2-20000000000000000000000
χ21222222-2-2-2-222-222-2-2-22-2000000000000000000002i−2i2i−2i000000
χ22222222-2-2-2-222-222-2-2-22-200000000000000000000−2i2i−2i2i000000
χ23222222-2-2-2-222-2-2-222-2-220000000000000000000000002i−2i2i−2i00
χ24222222-2-2-2-222-2-2-222-2-22000000000000000000000000−2i2i−2i2i00
χ25222222-2-2-2-2-2-2222-2-22-220000000000000000000000002-2-2200
χ26222222-2-2-2-2-2-2222-2-22-22000000000000000000000000-222-200
χ27222222-2-2-2-2-2-22-2-22222-2000000000000000000002-2-22000000
χ28222222-2-2-2-2-2-22-2-22222-200000000000000000000-222-2000000
χ292-2-22-22-2-2222-220000-20000002-22-20000i2−i2i2−i2i2−i2i2−i20000000000
χ302-2-22-22-2-2222-220000-20000002-22-20000−i2i2−i2i2−i2i2−i2i20000000000
χ312-2-22-22-2-2222-220000-2000000-22-220000i2−i2i2−i2−i2i2−i2i20000000000
χ322-2-22-22-2-2222-220000-2000000-22-220000−i2i2−i2i2i2−i2i2−i20000000000
χ332-2-22-22-2-222-22-2000020000002-2-2200002−2−222−2−220000000000
χ342-2-22-22-2-222-22-2000020000002-2-220000−222−2−222−20000000000
χ352-2-22-22-2-222-22-200002000000-222-200002−2−22−222−20000000000
χ362-2-22-22-2-222-22-200002000000-222-20000−222−22−2−220000000000
χ374444-4-44-44-40000000000004-400000000000000000000000000
χ384444-4-44-44-4000000000000-4400000000000000000000000000
χ394444-4-4-44-4400000000004-40000000000000000000000000000
χ404444-4-4-44-440000000000-440000000000000000000000000000
χ414-4-444-44-4-440004i−4i4i−4i000000000000000000000000000000000
χ424-4-444-44-4-44000−4i4i−4i4i000000000000000000000000000000000
χ434-4-444-4-444-40004i−4i−4i4i000000000000000000000000000000000
χ444-4-444-4-444-4000−4i4i4i−4i000000000000000000000000000000000
χ454-4-44-4444-4-44-4-40000400000000000000000000000000000000
χ464-4-44-4444-4-4-4440000-400000000000000000000000000000000
χ4788-8-80000000000000000000000000022−22000000000000000000
χ4888-8-800000000000000000000000000−2222000000000000000000
χ498-88-800000000000000000000000022−2200000000000000000000
χ508-88-8000000000000000000000000−222200000000000000000000

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