Finite Group Databasebeta

← Group #136012

Character table — Group #136012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order1222224444224488882244884444444444448888881616161616161616
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ5111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-111-11-11-111111-11-1-1-1ii−i−iii−i−iii−i−i1-1ii−i−i11-1-111-1-1
χ101111-1-1-111-11-11-111111-11-1-1-1ii−i−iii−i−i−i−iii1-1−i−iii-1-111-1-111
χ111111-1-1-111-11-11-111111-11-1-1-1−i−iii−i−iiiii−i−i1-1ii−i−i-1-111-1-111
χ121111-1-1-111-11-11-111111-11-1-1-1−i−iii−i−iii−i−iii1-1−i−iii11-1-111-1-1
χ131111-1-1-111-11-11-11111-11-11-1-1ii−i−i−i−iiiii−i−i-11−i−iii11-1-1-1-111
χ141111-1-1-111-11-11-11111-11-11-1-1ii−i−i−i−iii−i−iii-11ii−i−i-1-11111-1-1
χ151111-1-1-111-11-11-11111-11-11-1-1−i−iiiii−i−iii−i−i-11−i−iii-1-11111-1-1
χ161111-1-1-111-11-11-11111-11-11-1-1−i−iiiii−i−i−i−iii-11ii−i−i11-1-1-1-111
χ1722222222222222-2-2-2-22222-2-2000000000000-2-2000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-200000000000022000000000000
χ192222222222-2-2-2-222-2-200002-200002-22-2000000000000000000
χ202222222222-2-2-2-222-2-200002-20000-22-22000000000000000000
χ212222222222-2-2-2-2-2-2220000-222-22-20000000000000000000000
χ222222222222-2-2-2-2-2-2220000-22-22-220000000000000000000000
χ23222222-2-2-2-2-2-222000022-2-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ24222222-2-2-2-2-2-222000022-2-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ25222222-2-2-2-2-2-2220000-2-22200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ26222222-2-2-2-2-2-2220000-2-22200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ272222-2-22-2-22-222-200002-2-2200000000000000000000i2−i2−i2i2i2−i2−i2i2
χ282222-2-22-2-22-222-200002-2-2200000000000000000000−i2i2i2−i2−i2i2i2−i2
χ292222-2-22-2-22-222-20000-222-200000000000000000000i2−i2−i2i2−i2i2i2−i2
χ302222-2-22-2-22-222-20000-222-200000000000000000000−i2i2i2−i2i2−i2−i2i2
χ312222-2-2-222-22-22-2-2-2-2-22-22-222000000000000-22000000000000
χ322222-2-2-222-22-22-2-2-2-2-2-22-22220000000000002-2000000000000
χ332222-2-2-222-2-22-2222-2-20000-2200002i−2i−2i2i000000000000000000
χ342222-2-2-222-2-22-2222-2-20000-220000−2i2i2i−2i000000000000000000
χ352222-2-2-222-2-22-22-2-22200002-22i−2i−2i2i0000000000000000000000
χ362222-2-2-222-2-22-22-2-22200002-2−2i2i2i−2i0000000000000000000000
χ37444444-4-4-4-444-4-4000000000000000000000000000000000000
χ384444-4-44-4-444-4-44000000000000000000000000000000000000
χ394-4-444-444-4-400000000000000000000000000002i−2i2i−2i00000000
χ404-4-444-444-4-40000000000000000000000000000−2i2i−2i2i00000000
χ414-4-444-4-4-44400000000000000000000002-22-200000000000000
χ424-4-444-4-4-4440000000000000000000000-22-2200000000000000
χ434-4-44-444-44-400000000000000000000002i−2i−2i2i00000000000000
χ444-4-44-444-44-40000000000000000000000−2i2i2i−2i00000000000000
χ454-4-44-44-44-4400000000000000000000000000002-2-2200000000
χ464-4-44-44-44-440000000000000000000000000000-222-200000000
χ4788-8-80000000000004i2−4i200000000000000000000000000000000
χ4888-8-8000000000000−4i24i200000000000000000000000000000000
χ498-88-800000000004i2−4i20000000000000000000000000000000000
χ508-88-80000000000−4i24i20000000000000000000000000000000000

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