Finite Group Databasebeta

← Group #136191

Character table — Group #136191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444888888888888161616161616161616161616161616161616161616161616
order1222224444224444448888888844444444444444441616161616161616
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111
χ811111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ91-11-11-11-11-1-111-1ii−i−i1-1ii−i−i1-1i−i1-1i−ii−i1-1i−i11-1-1ii−i−i11-1-1
χ101-11-11-11-11-1-111-1ii−i−i1-1ii−i−i1-1i−i-11i−i−ii-11−ii11-1-1−i−iii-1-111
χ111-11-11-11-11-1-111-1ii−i−i1-1ii−i−i1-1−ii1-1−iii−i1-1i−i-1-111−i−iii-1-111
χ121-11-11-11-11-1-111-1ii−i−i1-1ii−i−i1-1−ii-11−ii−ii-11−ii-1-111ii−i−i11-1-1
χ131-11-11-11-11-1-111-1−i−iii1-1−i−iii1-1i−i1-1i−i−ii1-1−ii-1-111ii−i−i-1-111
χ141-11-11-11-11-1-111-1−i−iii1-1−i−iii1-1i−i-11i−ii−i-11i−i-1-111−i−iii11-1-1
χ151-11-11-11-11-1-111-1−i−iii1-1−i−iii1-1−ii1-1−ii−ii1-1−ii11-1-1−i−iii11-1-1
χ161-11-11-11-11-1-111-1−i−iii1-1−i−iii1-1−ii-11−iii−i-11i−i11-1-1ii−i−i-1-111
χ17222222222222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-22222-2-2000000000000000000000000
χ192222222222-2-2-2-200002-20000-2200220000-2-200000000000000
χ202222222222-2-2-2-200002-20000-2200-2-200002200000000000000
χ212222222222-2-2-2-20000-2200002-20000002200-2-2000000000000
χ222222222222-2-2-2-20000-2200002-2000000-2-20022000000000000
χ23222222-2-2-2-222-2-22-22-20000000000000000000000002−22−22−22−2
χ24222222-2-2-2-222-2-22-22-2000000000000000000000000−22−22−22−22
χ25222222-2-2-2-222-2-2-22-220000000000000000000000002−22−2−22−22
χ26222222-2-2-2-222-2-2-22-22000000000000000000000000−22−222−22−2
χ272-22-22-22-22-22-2-220000220000-2-2002-20000-2200000000000000
χ282-22-22-22-22-22-2-220000220000-2-200-2200002-200000000000000
χ292-22-22-22-22-22-2-220000-2-20000220000002i−2i00−2i2i000000000000
χ302-22-22-22-22-22-2-220000-2-2000022000000−2i2i002i−2i000000000000
χ312-22-22-22-22-2-222-22i2i−2i−2i-22−2i−2i2i2i-22000000000000000000000000
χ322-22-22-22-22-2-222-2−2i−2i2i2i-222i2i−2i−2i-22000000000000000000000000
χ332-22-22-2-22-22-22-222i−2i−2i2i000000000000000000000000i2−i2−i2i22−2−22
χ342-22-22-2-22-22-22-222i−2i−2i2i000000000000000000000000−i2i2i2−i2−222−2
χ352-22-22-2-22-22-22-22−2i2i2i−2i000000000000000000000000i2−i2−i2i2−222−2
χ362-22-22-2-22-22-22-22−2i2i2i−2i000000000000000000000000−i2i2i2−i22−2−22
χ37444444-4-4-4-4-4-444000000000000000000000000000000000000
χ384444-4-444-4-400000000000000000000000000002i−2i2i−2i00000000
χ394444-4-444-4-40000000000000000000000000000−2i2i−2i2i00000000
χ404444-4-4-4-44400000000000000002200-2-2000000000000000000
χ414444-4-4-4-4440000000000000000-2-20022000000000000000000
χ424-44-44-4-44-444-44-4000000000000000000000000000000000000
χ434-44-4-444-4-4400000000000000000000000000002i−2i−2i2i00000000
χ444-44-4-444-4-440000000000000000000000000000−2i2i2i−2i00000000
χ454-44-4-44-444-400000000000000002i−2i00−2i2i000000000000000000
χ464-44-4-44-444-40000000000000000−2i2i002i−2i000000000000000000
χ4788-8-8000000000000000022−2222−2200000000000000000000000000
χ4888-8-80000000000000000−2222−222200000000000000000000000000
χ498-8-8800000000000000002i2−2i2−2i22i200000000000000000000000000
χ508-8-880000000000000000−2i22i22i2−2i200000000000000000000000000

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