Finite Group Databasebeta

← Group #131663

Character table — Group #131663

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112244444444444488888161616161616161616161616161616161616161616163232
order1222442444448888882444822444444444488161616161616161688
χ111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ5111111111111111111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-11111-1-1
χ6111111111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-1-1-11-1-111-1-1111111-1-11111-1-1-1-1-1-1
χ8111111111111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111
χ9111111-111-1-1-111-1-1-1-11-1-111111-1-1-11-1ii−i−i1-1ii−i−iii−i−ii−i
χ10111111-111-1-1-111-1-1-1-11-1-111111-1-1-11-1−i−iii1-1−i−iii−i−iii−ii
χ11111111-111-1-1-111-1-1-1-11-1-111-1-1-1111-11ii−i−i1-1−i−iii−i−iiii−i
χ12111111-111-1-1-111-1-1-1-11-1-111-1-1-1111-11−i−iii1-1ii−i−iii−i−i−ii
χ13111111-111-1-1-111-1-1-1-1-111-1111-11-1-1-11ii−i−i-11−i−iiiii−i−i−ii
χ14111111-111-1-1-111-1-1-1-1-111-1111-11-1-1-11−i−iii-11ii−i−i−i−iiii−i
χ15111111-111-1-1-111-1-1-1-1-111-11-1-11-1111-1ii−i−i-11ii−i−i−i−iii−ii
χ16111111-111-1-1-111-1-1-1-1-111-11-1-11-1111-1−i−iii-11−i−iiiii−i−ii−i
χ17222222222222-2-2-2-2-2-22222-2000000000000-2-20000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2-2000000000000220000000000
χ192222222-2-2-22-222-222-20000-2002-200-220000000000000000
χ202222222-2-2-22-222-222-20000-200-22002-20000000000000000
χ212222222-2-2-22-2-2-22-2-22000022-2002-2000000000000000000
χ222222222-2-2-22-2-2-22-2-2200002-2200-22000000000000000000
χ23222222-222-2-2-2-2-222222-2-22-2000000000000-220000000000
χ24222222-222-2-2-2-2-22222-222-2-20000000000002-20000000000
χ25222222-2-2-22-22222-2-220000-2002200-2-20000000000000000
χ26222222-2-2-22-22222-2-220000-200-2-200220000000000000000
χ27222222-2-2-22-22-2-2-222-2000022-200-22000000000000000000
χ28222222-2-2-22-22-2-2-222-200002-22002-2000000000000000000
χ292222-2-222-2-2-220000002-22-20000000000000002−22−22−22−200
χ302222-2-222-2-2-220000002-22-2000000000000000−22−22−22−2200
χ312222-2-222-2-2-22000000-22-220000000000000002−22−2−22−2200
χ322222-2-222-2-2-22000000-22-22000000000000000−22−222−22−200
χ332222-2-2-22-222-200000022-2-2000000000000000i2−i2−i2i2i2−i2−i2i200
χ342222-2-2-22-222-200000022-2-2000000000000000−i2i2i2−i2−i2i2i2−i200
χ352222-2-2-22-222-2000000-2-222000000000000000i2−i2−i2i2−i2i2i2−i200
χ362222-2-2-22-222-2000000-2-222000000000000000−i2i2i2−i2i2−i2−i2i200
χ374444-4-44-444-4-400000000000000000000000000000000000
χ384444-4-4-4-44-44400000000000000000000000000000000000
χ394-4-444-400000000400-400000000000002i−2i2i−2i000000000000
χ404-4-444-400000000400-40000000000000−2i2i−2i2i000000000000
χ414-4-444-400000000-400400000000000002-2-22000000000000
χ424-4-444-400000000-40040000000000000-222-2000000000000
χ4388-8-80000000042−42000000000000000000000000000000000
χ4488-8-800000000−4242000000000000000000000000000000000
χ458-88-8000000000004i2−4i2000000000000000000000000000000
χ468-88-800000000000−4i24i2000000000000000000000000000000
χ478-8-88-8800000000000000000000000000000000000000000

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