Finite Group Databasebeta

← Group #136160

Character table — Group #136160

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ511111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111-1-1-1-1111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ811111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ911-11-1-11-11-11-11-1-111ii−i−i-1-11i−i1-1i−ii−i1-1i−ii−i11-1-1ii−i−i11-1-1
χ1011-11-1-11-11-11-11-1-111ii−i−i-1-11i−i-11i−i−ii-11i−i−ii11-1-1−i−iii-1-111
χ1111-11-1-11-11-11-11-1-111ii−i−i-1-11−ii1-1−iii−i1-1i−ii−i-1-111−i−iii-1-111
χ1211-11-1-11-11-11-11-1-111ii−i−i-1-11−ii-11−ii−ii-11i−i−ii-1-111ii−i−i11-1-1
χ1311-11-1-11-11-11-11-1-111−i−iii-1-11i−i1-1i−i−ii1-1−ii−ii-1-111ii−i−i-1-111
χ1411-11-1-11-11-11-11-1-111−i−iii-1-11i−i-11i−ii−i-11−iii−i-1-111−i−iii11-1-1
χ1511-11-1-11-11-11-11-1-111−i−iii-1-11−ii1-1−ii−ii1-1−ii−ii11-1-1−i−iii11-1-1
χ1611-11-1-11-11-11-11-1-111−i−iii-1-11−ii-11−iii−i-11−iii−i11-1-1ii−i−i-1-111
χ172222222222222222-22222-2-2-20000000000-2-200000000000000
χ182222222222222222-2-2-2-2-2-2-2-200000000002200000000000000
χ19222222222222-2-2-2-220000-22-200220000-2-20000000000000000
χ20222222222222-2-2-2-220000-22-200-2-20000220000000000000000
χ21222222222222-2-2-2-2-200002-22000000220000-2-2000000000000
χ22222222222222-2-2-2-2-200002-22000000-2-2000022000000000000
χ23222-22-2-2-222-2-222-2-202-22-20000000000000000000002−22−22−22−2
χ24222-22-2-2-222-2-222-2-202-22-2000000000000000000000−22−22−22−22
χ25222-22-2-2-222-2-222-2-20-22-220000000000000000000002−22−2−22−22
χ26222-22-2-2-222-2-222-2-20-22-22000000000000000000000−22−222−22−2
χ2722-22-2-22-22-22-22-2-22-22i2i−2i−2i22-20000000000−2i2i00000000000000
χ2822-22-2-22-22-22-22-2-22-2−2i−2i2i2i22-200000000002i−2i00000000000000
χ2922-22-2-22-22-22-2-222-2200002-2-2002-20000-220000000000000000
χ3022-22-2-22-22-22-2-222-2200002-2-200-2200002-20000000000000000
χ3122-22-2-22-22-22-2-222-2-20000-2220000002i−2i0000−2i2i000000000000
χ3222-22-2-22-22-22-2-222-2-20000-222000000−2i2i00002i−2i000000000000
χ3322-2-2-22-222-2-222-22-202i−2i−2i2i000000000000000000000i2−i2−i2i22−2−22
χ3422-2-2-22-222-2-222-22-202i−2i−2i2i000000000000000000000−i2i2i2−i2−222−2
χ3522-2-2-22-222-2-222-22-20−2i2i2i−2i000000000000000000000i2−i2−i2i2−222−2
χ3622-2-2-22-222-2-222-22-20−2i2i2i−2i000000000000000000000−i2i2i2−i22−2−22
χ3744444444-4-4-4-40000000000002200-2-200000000000000000000
χ3844444444-4-4-4-4000000000000-2-2002200000000000000000000
χ39444-44-4-4-444-4-4-4-4440000000000000000000000000000000000
χ40444-44-4-4-4-4-444000000000000000000000000002i−2i2i−2i00000000
χ41444-44-4-4-4-4-44400000000000000000000000000−2i2i−2i2i00000000
χ4244-44-4-44-4-44-440000000000002i−2i00−2i2i00000000000000000000
χ4344-44-4-44-4-44-44000000000000−2i2i002i−2i00000000000000000000
χ4444-4-4-44-444-4-44-44-440000000000000000000000000000000000
χ4544-4-4-44-44-444-4000000000000000000000000002i−2i−2i2i00000000
χ4644-4-4-44-44-444-400000000000000000000000000−2i2i2i−2i00000000
χ478-888-88-8-8000000000000000000000000000000000000000000
χ488-88-8-8-888000000000000000000000000000000000000000000
χ498-8-888-8-88000000000000000000000000000000000000000000
χ508-8-8-8888-8000000000000000000000000000000000000000000

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