Finite Group Databasebeta

← Group #136015

Character table — Group #136015

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order1222224444222222444488884444444488888888881616161616161616
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
χ5111111111111-1-1-1-111-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-111-1-11111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1
χ91-11-11-1-111-11-111-1-11-11-1-1-111i−ii−ii−ii−i1-1ii−i−iii−i−i11-1-111-1-1
χ101-11-11-1-111-11-111-1-11-11-1-1-111i−ii−ii−ii−i1-1−i−iii−i−iii-1-111-1-111
χ111-11-11-1-111-11-111-1-11-11-1-1-111−ii−ii−ii−ii1-1ii−i−iii−i−i-1-111-1-111
χ121-11-11-1-111-11-111-1-11-11-1-1-111−ii−ii−ii−ii1-1−i−iii−i−iii11-1-111-1-1
χ131-11-11-1-111-11-1-1-1111-1-11-1-111i−i−iii−i−ii-11ii−i−i−i−iii11-1-1-1-111
χ141-11-11-1-111-11-1-1-1111-1-11-1-111i−i−iii−i−ii-11−i−iiiii−i−i-1-11111-1-1
χ151-11-11-1-111-11-1-1-1111-1-11-1-111−iii−i−iii−i-11ii−i−i−i−iii-1-11111-1-1
χ161-11-11-1-111-11-1-1-1111-1-11-1-111−iii−i−iii−i-11−i−iiiii−i−i11-1-1-1-111
χ1722222222222222222222-2-2-2-200000000-2-20000000000000000
χ18222222222222-2-2-2-222-2-2-2-2-2-200000000220000000000000000
χ192222222222-2-20000-2-2002-22-2002200-2-2000000000000000000
χ202222222222-2-20000-2-2002-22-200-2-20022000000000000000000
χ212222222222-2-20000-2-200-22-222200-2-200000000000000000000
χ222222222222-2-20000-2-200-22-22-2-2002200000000000000000000
χ23222222-2-2-2-2222222-2-2-2-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ24222222-2-2-2-2222222-2-2-2-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ25222222-2-2-2-222-2-2-2-2-2-2220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ26222222-2-2-2-222-2-2-2-2-2-2220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ272-22-22-22-2-222-222-2-2-22-220000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ282-22-22-22-2-222-222-2-2-22-220000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ292-22-22-22-2-222-2-2-222-222-20000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ302-22-22-22-2-222-2-2-222-222-20000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ312-22-22-2-222-22-222-2-22-22-222-2-200000000-220000000000000000
χ322-22-22-2-222-22-2-2-2222-2-2222-2-2000000002-20000000000000000
χ332-22-22-2-222-2-220000-22002-2-222i−2i00−2i2i00000000000000000000
χ342-22-22-2-222-2-220000-22002-2-22−2i2i002i−2i00000000000000000000
χ352-22-22-2-222-2-220000-2200-222-2002i−2i00−2i2i000000000000000000
χ362-22-22-2-222-2-220000-2200-222-200−2i2i002i−2i000000000000000000
χ37444444-4-4-4-4-4-400004400000000000000000000000000000000
χ384444-4-444-4-40000000000000000000000002i−2i2i−2i000000000000
χ394444-4-444-4-4000000000000000000000000−2i2i−2i2i000000000000
χ404444-4-4-4-44400000000000000000000000000002-22-200000000
χ414444-4-4-4-4440000000000000000000000000000-22-2200000000
χ424-44-44-44-4-44-4400004-400000000000000000000000000000000
χ434-44-4-444-44-400000000000000000000000000002i−2i−2i2i00000000
χ444-44-4-444-44-40000000000000000000000000000−2i2i2i−2i00000000
χ454-44-4-44-44-440000000000000000000000002-2-22000000000000
χ464-44-4-44-44-44000000000000000000000000-222-2000000000000
χ4788-8-8000000004-44-40000000000000000000000000000000000
χ4888-8-800000000-44-440000000000000000000000000000000000
χ498-8-88000000004-4-440000000000000000000000000000000000
χ508-8-8800000000-444-40000000000000000000000000000000000

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