Finite Group Databasebeta

← Group #136183

Character table — Group #136183

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91-1111-1-1-11-11-11-1-111-1ii−i−iii−i−i11-1-1ii−i−i1-11-1i−ii−ii−i11-1-111-1-1ii−i−i
χ101-1111-1-1-11-11-11-1-111-1ii−i−iii−i−i11-1-1ii−i−i1-11-1−ii−iii−i-1-111-1-111−i−iii
χ111-1111-1-1-11-11-11-1-111-1ii−i−i−i−iii-1-111ii−i−i1-1-11i−ii−i−ii11-1-1-1-111−i−iii
χ121-1111-1-1-11-11-11-1-111-1ii−i−i−i−iii-1-111ii−i−i1-1-11−ii−ii−ii-1-11111-1-1ii−i−i
χ131-1111-1-1-11-11-11-1-111-1−i−iiiii−i−i-1-111−i−iii1-1-11i−ii−ii−i-1-11111-1-1−i−iii
χ141-1111-1-1-11-11-11-1-111-1−i−iiiii−i−i-1-111−i−iii1-1-11−ii−iii−i11-1-1-1-111ii−i−i
χ151-1111-1-1-11-11-11-1-111-1−i−iii−i−iii11-1-1−i−iii1-11-1i−ii−i−ii-1-111-1-111ii−i−i
χ161-1111-1-1-11-11-11-1-111-1−i−iii−i−iii11-1-1−i−iii1-11-1−ii−ii−ii11-1-111-1-1−i−iii
χ172222222222222222-2-2222200000000-2-2-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2000000002222-2-200000000000000000000
χ19222222222222-2-2-2-22-20000000022220000-22-2-2000000000000000000
χ20222222222222-2-2-2-22-200000000-2-2-2-20000-2222000000000000000000
χ21222222222222-2-2-2-2-2200002222000000002-2000000-2-2000000000000
χ22222222222222-2-2-2-2-220000-2-2-2-2000000002-200000022000000000000
χ2322-2-222-2-2-222-2-22-22000000000000002i−2i2i−2i000000000000002−22−2i2−i2i2−i2
χ2422-2-222-2-2-222-2-22-22000000000000002i−2i2i−2i00000000000000−22−22−i2i2−i2i2
χ2522-2-222-2-2-222-2-22-2200000000000000−2i2i−2i2i000000000000002−22−2−i2i2−i2i2
χ2622-2-222-2-2-222-2-22-2200000000000000−2i2i−2i2i00000000000000−22−22i2−i2i2−i2
χ272-2222-2-2-22-22-22-2-22-222i2i−2i−2i00000000−2i−2i2i2i-2200000000000000000000
χ282-2222-2-2-22-22-22-2-22-22−2i−2i2i2i000000002i2i−2i−2i-2200000000000000000000
χ292-2222-2-2-22-22-2-222-2220000000022-2-20000-2-2-22000000000000000000
χ302-2222-2-2-22-22-2-222-22200000000-2-2220000-2-22-2000000000000000000
χ312-2222-2-2-22-22-2-222-2-2-200002i2i−2i−2i0000000022000000−2i2i000000000000
χ322-2222-2-2-22-22-2-222-2-2-20000−2i−2i2i2i00000000220000002i−2i000000000000
χ332-2-2-22-222-2-222-2-222000000000000002-2-22000000000000002−2−222−2−22
χ342-2-2-22-222-2-222-2-222000000000000002-2-2200000000000000−222−2−222−2
χ352-2-2-22-222-2-222-2-22200000000000000-222-2000000000000002−2−22−222−2
χ362-2-2-22-222-2-222-2-22200000000000000-222-200000000000000−222−22−2−22
χ3744444444-4-4-4-40000000000000000000000000022-2-200000000000000
χ3844444444-4-4-4-400000000000000000000000000-2-22200000000000000
χ39444-4-4-4-4400000000002i−2i2i−2i2-22-22i−2i2i−2i00000000000000000000000000
χ40444-4-4-4-4400000000002i−2i2i−2i-22-22−2i2i−2i2i00000000000000000000000000
χ41444-4-4-4-440000000000−2i2i−2i2i2-22-2−2i2i−2i2i00000000000000000000000000
χ42444-4-4-4-440000000000−2i2i−2i2i-22-222i−2i2i−2i00000000000000000000000000
χ4344-4-444-4-44-4-44000000000000000000000000000000002i−2i2i−2i00000000
χ4444-4-444-4-44-4-4400000000000000000000000000000000−2i2i−2i2i00000000
χ4544-4-444-4-4-444-44-44-40000000000000000000000000000000000000000
χ464-4444-4-4-4-44-44000000000000000000000000002i−2i−2i2i00000000000000
χ474-4444-4-4-4-44-4400000000000000000000000000−2i2i2i−2i00000000000000
χ484-44-4-444-400000000002-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ494-44-4-444-400000000002-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ504-44-4-444-40000000000-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ514-44-4-444-40000000000-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ524-4-4-44-44444-4-4000000000000000000000000000000002i−2i−2i2i00000000
χ534-4-4-44-44444-4-400000000000000000000000000000000−2i2i2i−2i00000000
χ544-4-4-44-444-4-44444-4-40000000000000000000000000000000000000000
χ5588-88-8-88-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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