Finite Group Databasebeta

← Group #136133

Character table — Group #136133

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1
χ91-1-1111-1-111-1-11-1-111-1ii−i−i1-11-1i−ii−ii−ii−i1-1i−i11-1-1ii−i−i11-1-1
χ101-1-1111-1-111-1-11-1-111-1ii−i−i1-11-1−iii−i−iii−i1-1i−i-1-111−i−iii-1-111
χ111-1-1111-1-111-1-11-1-111-1ii−i−i1-1-11i−i−iii−ii−i-11−ii11-1-1−i−iii-1-111
χ121-1-1111-1-111-1-11-1-111-1ii−i−i1-1-11−ii−ii−iii−i-11−ii-1-111ii−i−i11-1-1
χ131-1-1111-1-111-1-11-1-111-1−i−iii1-11-1i−i−iii−i−ii1-1−ii-1-111ii−i−i-1-111
χ141-1-1111-1-111-1-11-1-111-1−i−iii1-11-1−ii−ii−ii−ii1-1−ii11-1-1−i−iii11-1-1
χ151-1-1111-1-111-1-11-1-111-1−i−iii1-1-11i−ii−ii−i−ii-11i−i-1-111−i−iii11-1-1
χ161-1-1111-1-111-1-11-1-111-1−i−iii1-1-11−iii−i−ii−ii-11i−i11-1-1ii−i−i-1-111
χ172222222222222222-2-22222-2-200000000-2-20000000000000000
χ182222222222222222-2-2-2-2-2-2-2-200000000220000000000000000
χ19222222222222-2-2-2-22-20000-222200000000-2-200000000000000
χ20222222222222-2-2-2-22-20000-22-2-2000000002200000000000000
χ21222222222222-2-2-2-2-2200002-2000022000000-2-2000000000000
χ22222222222222-2-2-2-2-2200002-20000-2-200000022000000000000
χ23222-2-22-2-2-222-2-22-22002i−2i2i−2i00000000000000000000i2−i2i2−i22−22−2
χ24222-2-22-2-2-222-2-22-22002i−2i2i−2i00000000000000000000−i2i2−i2i2−22−22
χ25222-2-22-2-2-222-2-22-2200−2i2i−2i2i00000000000000000000i2−i2i2−i2−22−22
χ26222-2-22-2-2-222-2-22-2200−2i2i−2i2i00000000000000000000−i2i2−i2i22−22−2
χ272-2-2222-2-222-2-22-2-22-222i2i−2i−2i-2200000000−2i2i0000000000000000
χ282-2-2222-2-222-2-22-2-22-22−2i−2i2i2i-22000000002i−2i0000000000000000
χ292-2-2222-2-222-2-2-222-2220000-2-22-200000000-2200000000000000
χ302-2-2222-2-222-2-2-222-2220000-2-2-22000000002-200000000000000
χ312-2-2222-2-222-2-2-222-2-2-200002200002i−2i000000−2i2i000000000000
χ322-2-2222-2-222-2-2-222-2-2-20000220000−2i2i0000002i−2i000000000000
χ332-2-2-2-2222-22-22-2-222002-2-22000000000000000000002−2−222−2−22
χ342-2-2-2-2222-22-22-2-222002-2-2200000000000000000000−222−2−222−2
χ352-2-2-2-2222-22-22-2-22200-222-2000000000000000000002−2−22−222−2
χ362-2-2-2-2222-22-22-2-22200-222-200000000000000000000−222−22−2−22
χ3744444444-4-4-4-4000000000000002200-2-2000000000000000000
χ3844444444-4-4-4-400000000000000-2-20022000000000000000000
χ39444-4-44-4-44-4-44000000000000000000000000002-22-200000000
χ40444-4-44-4-44-4-4400000000000000000000000000-22-2200000000
χ41444-4-44-4-4-444-44-44-40000000000000000000000000000000000
χ424-4-4444-4-4-4-444000000000000002i−2i00−2i2i000000000000000000
χ434-4-4444-4-4-4-44400000000000000−2i2i002i−2i000000000000000000
χ444-4-4-4-44444-44-4000000000000000000000000002-2-2200000000
χ454-4-4-4-44444-44-400000000000000000000000000-222-200000000
χ464-4-4-4-4444-44-4444-4-40000000000000000000000000000000000
χ4788-88-8-88-8000000000000000000000000000000000000000000
χ4888-8-88-8-88000000000000000000000000000000000000000000
χ498-888-8-8-88000000000000000000000000000000000000000000
χ508-88-88-88-8000000000000000000000000000000000000000000

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