Finite Group Databasebeta

← Group #138495

Character table — Group #138495

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444444444888888881616161616161616161616161616161632323232
order1222224444224444448888448888888888888816161616161616164444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-111-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111-1-111-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111111-1-1111-1-1-1-1-1-1-1-1-11-11111-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011111111-1-1111-1-1-1-1-1-1-1-1-11-11111-1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ1111111111-1-1111-1-1-1-1-1-1-1-1-11-11111-1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ1211111111-1-1111-1-1-1-1-1-1-1-1-11-11111-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ1311111111-1-1-1-11-111-1-1-1-1-1-1-1111-1-111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-11-111-1-1-1-1-1-1-1111-1-111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-11-111-1-1-1-1-1-1-1111-1-111−i−iiiii−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-11-111-1-1-1-1-1-1-1111-1-111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ17222222222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000
χ182222222222-2-222-2-222-2-2-2-2-2-2-2-2222200000000000000000000
χ1922222222-2-2222-2-2-2-2-222222-2-2-2-2-22200000000000000000000
χ2022222222-2-2-2-22-222-2-22222-22-2-222-2-200000000000000000000
χ21222222-2-22222-2222-2-20000-2-2000000000000002−22−22−22−20000
χ22222222-2-22222-2222-2-20000-2-200000000000000−22−22−22−220000
χ23222222-2-222-2-2-22-2-2-2-2000022000000000000002−22−2−22−220000
χ24222222-2-222-2-2-22-2-2-2-200002200000000000000−22−222−22−20000
χ25222222-2-2-2-222-2-2-2-2220000-2200000000000000i2−i2−i2i2i2−i2−i2i20000
χ26222222-2-2-2-222-2-2-2-2220000-2200000000000000−i2i2i2−i2−i2i2i2−i20000
χ27222222-2-2-2-2-2-2-2-2222200002-200000000000000i2−i2−i2i2−i2i2i2−i20000
χ28222222-2-2-2-2-2-2-2-2222200002-200000000000000−i2i2i2−i2i2−i2−i2i20000
χ292222-2-2222200-2-2002-222-2-2002-2000000002-22-2000000000000
χ302222-2-2222200-2-2002-222-2-2002-200000000-22-22000000000000
χ312222-2-2222200-2-2002-2-2-22200-2200002-22-20000000000000000
χ322222-2-2222200-2-2002-2-2-22200-220000-22-220000000000000000
χ332222-2-222-2-200-2200-2222-2-200-2200002i−2i−2i2i0000000000000000
χ342222-2-222-2-200-2200-2222-2-200-220000−2i2i2i−2i0000000000000000
χ352222-2-222-2-200-2200-22-2-222002-2000000002i−2i−2i2i000000000000
χ362222-2-222-2-200-2200-22-2-222002-200000000−2i2i2i−2i000000000000
χ374444-4-4-4-444004-400-4400000000000000000000000000000000
χ384444-4-4-4-4-4-40044004-400000000000000000000000000000000
χ394-4-444-4000000004i−4i0022−2222−2200002i2−2i20000000000000000000000
χ404-4-444-4000000004i−4i00−2222−22220000−2i22i20000000000000000000000
χ414-4-444-400000000−4i4i0022−2222−220000−2i22i20000000000000000000000
χ424-4-444-400000000−4i4i00−2222−222200002i2−2i20000000000000000000000
χ434-4-44-4400004-400000022−22−222200000022−2200000000000000000000
χ444-4-44-4400004-4000000−222222−22000000−222200000000000000000000
χ454-4-44-440000-4400000022−22−2222000000−222200000000000000000000
χ464-4-44-440000-44000000−222222−2200000022−2200000000000000000000
χ4788-8-800008-80000000000000000000000000000000000000000
χ4888-8-80000-880000000000000000000000000000000000000000
χ498-88-8008-8000000000000000000000000000000000000000000
χ508-88-800-88000000000000000000000000000000000000000000

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