Finite Group Databasebeta

← Group #72265789

Character table — Group #72265789

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size111122222222224444448888888888888888881616161616161616161616163232323232323232323232323232323232323232
order1222222222222222222222222222222222444422444444444444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-22222222222-2-2-2-200-2-2-2-200000000000000000000000000
χ1822222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-200222200000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200-2-22200000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220022-2-200000000000000000000000000
χ21222222222-2-2-2-22-2-2222222-2-2-2-2000000002-22-2000000000000000000002-22-200000000
χ22222222222-2-2-2-22-2-2222222-2-2-2-2000000002-22-200000000000000000000-22-2200000000
χ23222222222-2-2-2-22-2-22222-2-222-2-200000000-22-2200000000000000002-22-2000000000000
χ24222222222-2-2-2-22-2-22222-2-222-2-200000000-22-220000000000000000-22-22000000000000
χ25222222222-2-2-2-22-2-2-2-2-2-222-2-22200000000-22-22000000000000000000002i−2i−2i2i00000000
χ26222222222-2-2-2-22-2-2-2-2-2-222-2-22200000000-22-2200000000000000000000−2i2i2i−2i00000000
χ27222222222-2-2-2-22-2-2-2-2-2-2-2-22222000000002-22-200000000000000002i−2i−2i2i000000000000
χ28222222222-2-2-2-22-2-2-2-2-2-2-2-22222000000002-22-20000000000000000−2i2i2i−2i000000000000
χ2922222-2-2-2-222222-2-222-2-22-22-22-2000000002-2-220000000000002-22-20000000000000000
χ3022222-2-2-2-222222-2-222-2-22-22-22-2000000002-2-22000000000000-22-220000000000000000
χ3122222-2-2-2-222222-2-222-2-2-22-222-200000000-222-2220000-2-222-2-200000000000000000000
χ3222222-2-2-2-222222-2-222-2-2-22-222-200000000-222-2-2-2000022-2-22200000000000000000000
χ3322222-2-2-2-222222-2-2-2-2222-22-2-2200000000-222-20000000000002-2-220000000000000000
χ3422222-2-2-2-222222-2-2-2-2222-22-2-2200000000-222-2000000000000-222-20000000000000000
χ3522222-2-2-2-222222-2-2-2-222-22-22-22000000002-2-22220000-2-2-2-22200000000000000000000
χ3622222-2-2-2-222222-2-2-2-222-22-22-22000000002-2-22-2-200002222-2-200000000000000000000
χ3722222-2-2-2-2-2-2-2-222222-2-22-2-22-220000000022-2-20000000000000000000000002i−2i2i−2i0000
χ3822222-2-2-2-2-2-2-2-222222-2-22-2-22-220000000022-2-2000000000000000000000000−2i2i−2i2i0000
χ3922222-2-2-2-2-2-2-2-222222-2-2-222-2-2200000000-2-22200000000000000000000000000002-22-2
χ4022222-2-2-2-2-2-2-2-222222-2-2-222-2-2200000000-2-2220000000000000000000000000000-22-22
χ4122222-2-2-2-2-2-2-2-2222-2-2222-2-222-200000000-2-2220000000000000000000000002-2-220000
χ4222222-2-2-2-2-2-2-2-2222-2-2222-2-222-200000000-2-222000000000000000000000000-222-20000
χ4322222-2-2-2-2-2-2-2-2222-2-222-222-22-20000000022-2-200000000000000000000000000002i−2i−2i2i
χ4422222-2-2-2-2-2-2-2-2222-2-222-222-22-20000000022-2-20000000000000000000000000000−2i2i2i−2i
χ454444-444-4-444-4-4-44-4000000000000000000000000004-400000000000000000000000000
χ464444-444-4-444-4-4-44-400000000000000000000000000-4400000000000000000000000000
χ474444-444-4-4-4-444-4-440000000000000000000000004-40000000000000000000000000000
χ484444-444-4-4-4-444-4-44000000000000000000000000-440000000000000000000000000000
χ494444-4-4-44444-4-4-4-440000000000000044-4-4000000000000000000000000000000000000
χ504444-4-4-44444-4-4-4-4400000000000000-4-444000000000000000000000000000000000000
χ514444-4-4-444-4-444-44-4000000000044-4-40000000000000000000000000000000000000000
χ524444-4-4-444-4-444-44-40000000000-4-4440000000000000000000000000000000000000000
χ534-4-44-44-44-400004004-44-40000000000000000002-200002-22-22-200000000000000000000
χ544-4-44-44-44-400004004-44-4000000000000000000-220000-22-22-2200000000000000000000
χ554-4-44-44-44-40000400-44-440000000000000000002-200002-2-22-2200000000000000000000
χ564-4-44-44-44-40000400-44-44000000000000000000-220000-222-22-200000000000000000000
χ574-4-44-4-44-4400004004-4-440000000000000000002-20000-222-2-2200000000000000000000
χ584-4-44-4-44-4400004004-4-44000000000000000000-2200002-2-222-200000000000000000000
χ594-4-44-4-44-440000400-444-40000000000000000002-20000-22-222-200000000000000000000
χ604-4-44-4-44-440000400-444-4000000000000000000-2200002-22-2-2200000000000000000000
χ6188-8-800000008-8000000000000000004-44-4000000000000000000000000000000000000
χ6288-8-800000008-800000000000000000-44-44000000000000000000000000000000000000
χ6388-8-80000000-88000000000000000004-4-44000000000000000000000000000000000000
χ6488-8-80000000-8800000000000000000-444-4000000000000000000000000000000000000
χ658-88-8000008-80000000000000004-44-40000000000000000000000000000000000000000
χ668-88-8000008-8000000000000000-44-440000000000000000000000000000000000000000
χ678-88-800000-880000000000000004-4-440000000000000000000000000000000000000000
χ688-88-800000-88000000000000000-444-40000000000000000000000000000000000000000
χ698-8-8888-8-880000-800000000000000000000000000000000000000000000000000000000
χ708-8-888-888-80000-800000000000000000000000000000000000000000000000000000000

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