Finite Group Databasebeta

← Group #131621

Character table — Group #131621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444888888888888161616161616161616161616161616161616161616161616
order12222244442244444444444444222444448888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111-1-11-1-1111111-111-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111-1-11-1-1111111-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111-1-11-1-1-1-1-1-111-1-1-111-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-11-1-1-1-1-1-111-1-1-111-111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-111-1-11111-1-111-1-1-1-1-11-11-111-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-111-1-11111-1-111-1-1-1-1-11-11-111-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11-111-11ii−i−i−i−iiiii−i−i−i−iii
χ12111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11-111-11−i−iiiii−i−i−i−iiiii−i−i
χ13111111-1-1-1-111-1-11-1-111111-1-1-1-111-1-11-1-11ii−i−iii−i−i−i−iii−i−iii
χ14111111-1-1-1-111-1-11-1-111111-1-1-1-111-1-11-1-11−i−iii−i−iiiii−i−iii−i−i
χ15111111-1-1-1-111-1-11-1-1111-1-111-1-11-111-1-11-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-111-1-11-1-1111-1-111-1-11-111-1-11-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-200-2002222-2-20-2-2000000000000000000000
χ1822222222222222-200-200-2-2-2-2-2-2022000000000000000000000
χ192222222222-2-2-2-2222-2-2-20000-2220000-2000000000000000000
χ202222222222-2-2-2-22-2-2-2220000-22-200002000000000000000000
χ212222222222-2-2-2-2-20020000002-2000220-2-20000000000000000
χ222222222222-2-2-2-2-20020000002-2000-2-20220000000000000000
χ23222222-2-2-2-222-2-2-200-20022-2-2220-22000000000000000000000
χ24222222-2-2-2-222-2-2-200-200-2-2222202-2000000000000000000000
χ25222222-2-2-2-2-2-222222-22200002-2-20000-2000000000000000000
χ26222222-2-2-2-2-2-2222-2-2-2-2-200002-2200002000000000000000000
χ27222222-2-2-2-2-2-222-2002000000-220002-20-220000000000000000
χ28222222-2-2-2-2-2-222-2002000000-22000-2202-20000000000000000
χ292-22-22-222-2-22-2-220000002i−2i2i−2i000000000000000000i2−i2i2−i22−22−2
χ302-22-22-222-2-22-2-220000002i−2i2i−2i000000000000000000−i2i2−i2i2−22−22
χ312-22-22-222-2-22-2-22000000−2i2i−2i2i000000000000000000i2−i2i2−i2−22−22
χ322-22-22-222-2-22-2-22000000−2i2i−2i2i000000000000000000−i2i2−i2i22−22−2
χ332-22-22-2-2-2222-22-20000002i−2i−2i2i0000000000000000002−2−22−i2i2i2−i2
χ342-22-22-2-2-2222-22-20000002i−2i−2i2i000000000000000000−222−2i2−i2−i2i2
χ352-22-22-2-2-2222-22-2000000−2i2i2i−2i0000000000000000002−2−22i2−i2−i2i2
χ362-22-22-2-2-2222-22-2000000−2i2i2i−2i000000000000000000−222−2−i2i2i2−i2
χ374444-4-44-44-40000000000000000000000002i−2i2i−2i000000000000
χ384444-4-44-44-4000000000000000000000000−2i2i−2i2i000000000000
χ394444-4-4-44-440000000000000000000000002-2-22000000000000
χ404444-4-4-44-44000000000000000000000000-222-2000000000000
χ414-44-44-444-4-4-444-4000000000000000000000000000000000000
χ424-44-44-4-4-444-44-44000000000000000000000000000000000000
χ434-44-4-444-4-4400000000000000000000000000002-22-200000000
χ444-44-4-444-4-440000000000000000000000000000-22-2200000000
χ454-44-4-44-444-400000000000000000000000000002i−2i−2i2i00000000
χ464-44-4-44-444-40000000000000000000000000000−2i2i2i−2i00000000
χ4788-8-8000000000004i−4i000000000000000000000000000000000
χ4888-8-800000000000−4i4i000000000000000000000000000000000
χ498-8-88000000000000004-4000000000000000000000000000000
χ508-8-8800000000000000-44000000000000000000000000000000

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