Finite Group Databasebeta

← Group #136271

Character table — Group #136271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order1222224444224488884444882244444488888888881616161616161616
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-11-11-11-1-1111-1-1ii−i−i1-11-11-1i−ii−ii−iii−i−i11-1-1ii−i−i11-1-1
χ101111-1-11-11-11-1-1111-1-1ii−i−i1-11-11-1i−ii−ii−i−i−iii-1-111−i−iii-1-111
χ111111-1-11-11-11-1-1111-1-1ii−i−i1-1-11-11−ii−iii−iii−i−i11-1-1−i−iii-1-111
χ121111-1-11-11-11-1-1111-1-1ii−i−i1-1-11-11−ii−iii−i−i−iii-1-111ii−i−i11-1-1
χ131111-1-11-11-11-1-1111-1-1−i−iii1-11-11-1−ii−ii−iiii−i−i-1-111ii−i−i-1-111
χ141111-1-11-11-11-1-1111-1-1−i−iii1-11-11-1−ii−ii−ii−i−iii11-1-1−i−iii11-1-1
χ151111-1-11-11-11-1-1111-1-1−i−iii1-1-11-11i−ii−i−iiii−i−i-1-111−i−iii11-1-1
χ161111-1-11-11-11-1-1111-1-1−i−iii1-1-11-11i−ii−i−ii−i−iii11-1-1ii−i−i-1-111
χ1722222222222222-2-2-2-22222-2-200000000-2-20000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-200000000220000000000000000
χ192222222222-2-2-2-222-2-20000-22000022-2-2000000000000000000
χ202222222222-2-2-2-222-2-20000-220000-2-222000000000000000000
χ212222222222-2-2-2-2-2-22200002-222-2-20000000000000000000000
χ222222222222-2-2-2-2-2-22200002-2-2-2220000000000000000000000
χ23222222-2-2-2-222-2-200002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ24222222-2-2-2-222-2-200002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ25222222-2-2-2-222-2-20000-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ26222222-2-2-2-222-2-20000-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ272222-2-22-22-22-2-22-2-2222i2i−2i−2i-2200000000−2i2i0000000000000000
χ282222-2-22-22-22-2-22-2-222−2i−2i2i2i-22000000002i−2i0000000000000000
χ292222-2-22-22-2-222-222220000-2-200002i−2i−2i2i000000000000000000
χ302222-2-22-22-2-222-222220000-2-20000−2i2i2i−2i000000000000000000
χ312222-2-22-22-2-222-2-2-2-2-20000222-2-220000000000000000000000
χ322222-2-22-22-2-222-2-2-2-2-2000022-222-20000000000000000000000
χ332222-2-2-22-222-22-200002i−2i−2i2i000000000000000000002−2−22−i2i2i2−i2
χ342222-2-2-22-222-22-200002i−2i−2i2i00000000000000000000−222−2i2−i2−i2i2
χ352222-2-2-22-222-22-20000−2i2i2i−2i000000000000000000002−2−22i2−i2−i2i2
χ362222-2-2-22-222-22-20000−2i2i2i−2i00000000000000000000−222−2−i2i2i2−i2
χ37444444-4-4-4-4-4-444000000000000000000000000000000000000
χ384444-4-4-44-44-44-44000000000000000000000000000000000000
χ394-44-44-444-4-400000000000000000000000000002-22-200000000
χ404-44-44-444-4-40000000000000000000000000000-22-2200000000
χ414-44-44-4-4-4440000000000000000000000002-22-2000000000000
χ424-44-44-4-4-444000000000000000000000000-22-22000000000000
χ434-44-4-444-4-4400000000000000000000000000002-2-2200000000
χ444-44-4-444-4-440000000000000000000000000000-222-200000000
χ454-44-4-44-444-40000000000000000000000002i−2i−2i2i000000000000
χ464-44-4-44-444-4000000000000000000000000−2i2i2i−2i000000000000
χ4788-8-800000000004i2−4i20000000000000000000000000000000000
χ4888-8-80000000000−4i24i20000000000000000000000000000000000
χ498-8-8800000000000042−4200000000000000000000000000000000
χ508-8-88000000000000−424200000000000000000000000000000000

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