Finite Group Databasebeta

← Group #456722

Character table — Group #456722

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111111111111122222222888888888888888888888888888816161616161616161616161616161616
order12222222222222224444444422444444444488888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ511111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ611111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ711111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1
χ811111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111
χ9111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1
χ10111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ11111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ12111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111
χ15111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1
χ172222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-22200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000000000
χ212222-2-22222-2-2-2-2-2-2222-2-2-2-2200000000000000000000000022-2-200002i−2i2i−2i00000000
χ222222-2-22222-2-2-2-2-2-2222-2-2-2-2200000000000000000000000022-2-20000−2i2i−2i2i00000000
χ232222-2-22222-2-2-2-2-2-2222-2-2-2-22000000000000000000000000-2-22200002i−2i−2i2i00000000
χ242222-2-22222-2-2-2-2-2-2222-2-2-2-22000000000000000000000000-2-2220000−2i2i2i−2i00000000
χ25222-22-2-2-22-22-2-2-22222-22-2-22-2000000000000000000002i2i−2i−2i000000000000002i−2i2-200
χ26222-22-2-2-22-22-2-2-22222-22-2-22-2000000000000000000002i2i−2i−2i00000000000000−2i2i-2200
χ27222-22-2-2-22-22-2-2-22222-22-2-22-200000000000000000000−2i−2i2i2i000000000000002i−2i-2200
χ28222-22-2-2-22-22-2-2-22222-22-2-22-200000000000000000000−2i−2i2i2i00000000000000−2i2i2-200
χ292-2-22-2-2-2-222-222-2222-2-222-2-22000000000000000000002-22-200002-20000002-2000000
χ302-2-22-2-2-2-222-222-2222-2-222-2-22000000000000000000002-22-20000-22000000-22000000
χ312-2-22-2-2-2-222-222-2222-2-222-2-2200000000000000000000-22-2200002-2000000-22000000
χ322-2-22-2-2-2-222-222-2222-2-222-2-2200000000000000000000-22-220000-220000002-2000000
χ332-2-2-22-2222-2222-2-2-22-22-22-22-20000000000000000000000002i−2i2i−2i002-200000000002i−2i
χ342-2-2-22-2222-2222-2-2-22-22-22-22-20000000000000000000000002i−2i2i−2i00-220000000000−2i2i
χ352-2-2-22-2222-2222-2-2-22-22-22-22-2000000000000000000000000−2i2i−2i2i002-20000000000−2i2i
χ362-2-2-22-2222-2222-2-2-22-22-22-22-2000000000000000000000000−2i2i−2i2i00-2200000000002i−2i
χ372-2-2-2-22222-2-2-2-22222-222-22-2-22-200002-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ382-2-2-2-22222-2-2-2-22222-222-22-2-22-200002-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ392-2-2-2-22222-2-2-2-22222-222-22-2-2-220000-220000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ402-2-2-2-22222-2-2-2-22222-222-22-2-2-220000-22000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ412-2-2-2-22222-2-2-2-2222-22-2-22-2222-20000-22000022-2-222-2-2000000000000000000000000
χ422-2-2-2-22222-2-2-2-2222-22-2-22-2222-20000-220000-2-222-2-222000000000000000000000000
χ432-2-2-2-22222-2-2-2-2222-22-2-22-222-2200002-2000022-2-2-2-222000000000000000000000000
χ442-2-2-2-22222-2-2-2-2222-22-2-22-222-2200002-20000-2-22222-2-2000000000000000000000000
χ454444-4-44444-4-4-4-4-4-4-4-4-44444-400000000000000000000000000000000000000000000
χ46444-44-4-4-44-44-4-4-444-4-44-444-4400000000000000000000000000000000000000000000
χ47444-4-44-4-44-4-4444-4-444-4-444-4-400000000000000000000000000000000000000000000
χ48444-4-44-4-44-4-4444-4-4-4-444-4-44400000000000000000000000000000000000000000000
χ4944-444-44-4-4-4-44-444-40000000000000000004i−4i00000000000000000000000000000000
χ5044-444-44-4-4-4-44-444-4000000000000000000−4i4i00000000000000000000000000000000
χ5144-44-444-4-4-44-44-4-44000000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ5244-44-444-4-4-44-44-4-4400000000000000000000−2i22i2−2i22i20000000000000000000000000000
χ5344-4-444-44-44-4-44-44-40000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ5444-4-444-44-44-4-44-44-4000000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ5544-4-4-4-4-44-4444-44-440000000000004-400000000000000000000000000000000000000
χ5644-4-4-4-4-44-4444-44-44000000000000-4400000000000000000000000000000000000000
χ574-4444-4-44-4-4-4-444-4400000000004i−4i0000000000000000000000000000000000000000
χ584-4444-4-44-4-4-4-444-440000000000−4i4i0000000000000000000000000000000000000000
χ594-444-44-44-4-444-4-44-40000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ604-444-44-44-4-444-4-44-4000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ614-44-4444-4-44-44-4-4-44000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ624-44-4444-4-44-44-4-4-4400000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ634-44-4-4-44-4-444-4444-400000000000000004-40000000000000000000000000000000000
χ644-44-4-4-44-4-444-4444-40000000000000000-440000000000000000000000000000000000
χ654-4-4444-4-4444-4-44-4-44-4-4-4-444400000000000000000000000000000000000000000000
χ664-4-4444-4-4444-4-44-4-4-44444-4-4-400000000000000000000000000000000000000000000
χ674-4-44-4-4-4-444-444-444-444-4-444-400000000000000000000000000000000000000000000
χ684-4-4-44-4444-4444-4-4-4-44-44-44-4400000000000000000000000000000000000000000000

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