Finite Group Databasebeta

← Group #136205

Character table — Group #136205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1
χ9111-1-1-1-1111-1-11-1-111-1ii−i−iii−i−i11-1-1ii−i−i1-1ii−i−ii−i1-111-1-111-1-1ii−i−i
χ10111-1-1-1-1111-1-11-1-111-1ii−i−iii−i−i11-1-1ii−i−i1-1−i−iiii−i1-1-1-111-1-111−i−iii
χ11111-1-1-1-1111-1-11-1-111-1ii−i−i−i−iii-1-111ii−i−i1-1ii−i−i−ii-1111-1-1-1-111−i−iii
χ12111-1-1-1-1111-1-11-1-111-1ii−i−i−i−iii-1-111ii−i−i1-1−i−iii−ii-11-1-11111-1-1ii−i−i
χ13111-1-1-1-1111-1-11-1-111-1−i−iiiii−i−i-1-111−i−iii1-1ii−i−ii−i-11-1-11111-1-1−i−iii
χ14111-1-1-1-1111-1-11-1-111-1−i−iiiii−i−i-1-111−i−iii1-1−i−iiii−i-1111-1-1-1-111ii−i−i
χ15111-1-1-1-1111-1-11-1-111-1−i−iii−i−iii11-1-1−i−iii1-1ii−i−i−ii1-1-1-111-1-111ii−i−i
χ16111-1-1-1-1111-1-11-1-111-1−i−iii−i−iii11-1-1−i−iii1-1−i−iii−ii1-111-1-111-1-1−i−iii
χ172222222222222222-2-2222200000000-2-2-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2000000002222-2-200000000000000000000
χ19222222222222-2-2-2-22-20000000022220000-22000000-2-2000000000000
χ20222222222222-2-2-2-22-200000000-2-2-2-20000-2200000022000000000000
χ21222222222222-2-2-2-2-2200002222000000002-20000-2-200000000000000
χ22222222222222-2-2-2-2-220000-2-2-2-2000000002-200002200000000000000
χ23222-2-2-2-2222-2-22-2-22-222i2i−2i−2i00000000−2i−2i2i2i-2200000000000000000000
χ24222-2-2-2-2222-2-22-2-22-22−2i−2i2i2i000000002i2i−2i−2i-2200000000000000000000
χ25222-2-2-2-2222-2-2-222-2220000000022-2-20000-2-2000000-22000000000000
χ26222-2-2-2-2222-2-2-222-22200000000-2-2220000-2-20000002-2000000000000
χ27222-2-2-2-2222-2-2-222-2-2-200002i2i−2i−2i00000000220000−2i2i00000000000000
χ28222-2-2-2-2222-2-2-222-2-2-20000−2i−2i2i2i000000002200002i−2i00000000000000
χ292-2-222-2-22-222-222-2-2002-22-200000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-2-222-2-22-222-222-2-2002-22-200000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-2-222-2-22-222-222-2-200-22-2200000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-2-222-2-22-222-222-2-200-22-2200000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-2-2-2222-22-222-22-2002i−2i−2i2i00000000000000000000000000i2−i2−i2i2−222−2
χ342-2-2-2-2222-22-222-22-2002i−2i−2i2i00000000000000000000000000−i2i2i2−i22−2−22
χ352-2-2-2-2222-22-222-22-200−2i2i2i−2i00000000000000000000000000i2−i2−i2i22−2−22
χ362-2-2-2-2222-22-222-22-200−2i2i2i−2i00000000000000000000000000−i2i2i2−i2−222−2
χ3744444444-4-4-4-40000000000000000000000002-22-20000000000000000
χ3844444444-4-4-4-4000000000000000000000000-22-220000000000000000
χ39444-4-4-4-44-4-4440000000000000000000000002i−2i−2i2i0000000000000000
χ40444-4-4-4-44-4-444000000000000000000000000−2i2i2i−2i0000000000000000
χ414-444-44-4-4000000000000002i−2i2i−2i2i−2i2i−2i2-22-20000000000000000000000
χ424-444-44-4-4000000000000002i−2i2i−2i−2i2i−2i2i-22-220000000000000000000000
χ434-444-44-4-400000000000000−2i2i−2i2i2i−2i2i−2i-22-220000000000000000000000
χ444-444-44-4-400000000000000−2i2i−2i2i−2i2i−2i2i2-22-20000000000000000000000
χ454-44-44-44-4000000000000002-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ464-44-44-44-4000000000000002-2-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ474-44-44-44-400000000000000-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ484-44-44-44-400000000000000-222-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ494-4-444-4-444-4-44000000000000000000000000000000002i−2i2i−2i00000000
χ504-4-444-4-444-4-4400000000000000000000000000000000−2i2i−2i2i00000000
χ514-4-444-4-44-444-4-4-4440000000000000000000000000000000000000000
χ524-4-4-4-44444-44-4000000000000000000000000000000002i−2i−2i2i00000000
χ534-4-4-4-44444-44-400000000000000000000000000000000−2i2i2i−2i00000000
χ544-4-4-4-4444-44-44-44-440000000000000000000000000000000000000000
χ5588-88-8-88-8000000000000000000000000000000000000000000000000
χ5688-8-888-8-8000000000000000000000000000000000000000000000000

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