Finite Group Databasebeta

← Group #136242

Character table — Group #136242

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ9111-1-1-1-1111-1-11-1-111-1ii−i−i1-1i−iii−i−ii−i1-1i−i1-111-1-111-1-1ii−i−i
χ10111-1-1-1-1111-1-11-1-111-1ii−i−i1-1i−iii−i−i−ii-11−ii-1111-1-1-1-111−i−iii
χ11111-1-1-1-1111-1-11-1-111-1ii−i−i1-1i−i−i−iiii−i1-1i−i1-1-1-111-1-111−i−iii
χ12111-1-1-1-1111-1-11-1-111-1ii−i−i1-1i−i−i−iii−ii-11−ii-11-1-11111-1-1ii−i−i
χ13111-1-1-1-1111-1-11-1-111-1−i−iii1-1−iiii−i−ii−i-11i−i-11-1-11111-1-1−i−iii
χ14111-1-1-1-1111-1-11-1-111-1−i−iii1-1−iiii−i−i−ii1-1−ii1-1-1-111-1-111ii−i−i
χ15111-1-1-1-1111-1-11-1-111-1−i−iii1-1−ii−i−iiii−i-11i−i-1111-1-1-1-111ii−i−i
χ16111-1-1-1-1111-1-11-1-111-1−i−iii1-1−ii−i−iii−ii1-1−ii1-111-1-111-1-1−i−iii
χ172222222222222222-2-22222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-22-20000-22000000002200-2-2000000000000
χ20222222222222-2-2-2-22-20000-2200000000-2-20022000000000000
χ21222222222222-2-2-2-2-2200002-20000002200-2-200000000000000
χ22222222222222-2-2-2-2-2200002-2000000-2-2002200000000000000
χ23222-2-2-2-2222-2-22-2-22-222i2i−2i−2i-22−2i2i000000000000000000000000
χ24222-2-2-2-2222-2-22-2-22-22−2i−2i2i2i-222i−2i000000000000000000000000
χ25222-2-2-2-2222-2-2-222-2220000-2-2000000002-200-22000000000000
χ26222-2-2-2-2222-2-2-222-2220000-2-200000000-22002-2000000000000
χ27222-2-2-2-2222-2-2-222-2-2-20000220000002i−2i00−2i2i00000000000000
χ28222-2-2-2-2222-2-2-222-2-2-2000022000000−2i2i002i−2i00000000000000
χ292-2222-2-2-22-22-2-22-22002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-2222-2-2-22-22-2-22-22002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-2222-2-2-22-22-2-22-2200-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-2222-2-2-22-22-2-22-2200-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-22-2-222-22-2-22-2-222002i−2i−2i2i00000000000000000000i2−i2−i2i2−222−2
χ342-22-2-222-22-2-22-2-222002i−2i−2i2i00000000000000000000−i2i2i2−i22−2−22
χ352-22-2-222-22-2-22-2-22200−2i2i2i−2i00000000000000000000i2−i2−i2i22−2−22
χ362-22-2-222-22-2-22-2-22200−2i2i2i−2i00000000000000000000−i2i2i2−i2−222−2
χ3744444444-4-4-4-4000000000000002-22-200000000000000000000
χ3844444444-4-4-4-400000000000000-22-2200000000000000000000
χ39444-4-4-4-44-4-444000000000000002i−2i−2i2i00000000000000000000
χ40444-4-4-4-44-4-44400000000000000−2i2i2i−2i00000000000000000000
χ414-4444-4-4-44-44-44-44-40000000000000000000000000000000000
χ424-4444-4-4-4-44-44000000000000000000000000002i−2i2i−2i00000000
χ434-4444-4-4-4-44-4400000000000000000000000000−2i2i−2i2i00000000
χ444-44-4-444-44-4-4444-4-40000000000000000000000000000000000
χ454-44-4-444-4-444-4000000000000000000000000002i−2i−2i2i00000000
χ464-44-4-444-4-444-400000000000000000000000000−2i2i2i−2i00000000
χ4788-88-88-8-8000000000000000000000000000000000000000000
χ4888-8-88-88-8000000000000000000000000000000000000000000
χ498-8-88-8-888000000000000000000000000000000000000000000
χ508-8-8-888-88000000000000000000000000000000000000000000

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