Finite Group Databasebeta

← Group #251070

Character table — Group #251070

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444444444244444444888888222224444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1-1111-1-1-1-1111-1-1-1-1-1-1
χ311111111111111111111111-1-11-1-111111-1-1-1-11-1-1-111-1-1-1-1-1-1-1111
χ411111111111111111111111-1-11-1-1-1-1-1-11-11111-1-11-1-11-1-1-1111-1-1-1
χ511111111111111111-11-111-111-1-1-11111-1111-1-111-111-1-1-1-111-1-1-1-1
χ611111111111111111-11-111-111-1-1-1-1-1-1-1-11-1-11-1111-1-11-1-1-1-1-11111
χ711111111111111111-11-111-1-1-1-1111111-1-1-1-11-1-1-11111111-1-11-1-1-1
χ811111111111111111-11-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1111
χ91111111111111-1-1111-11-1-11111111111-11-1-1-1-1-1-1-1-1-111-1-111111-1
χ101111111111111-1-1111-11-1-1111111-1-1-1-1-11111-1-1-1111-11-1-1-1-1-1-1-11
χ111111111111111-1-1111-11-1-11-1-11-1-11111-1-1111-1111-1-1-1-111-1-1-111-1
χ121111111111111-1-1111-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1111-111111-1-11
χ131111111111111-1-111-1-1-1-1-1-111-1-1-1111111-1-111-1-11-1-1-1-11111-1-1-11
χ141111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11111-11-1-1-1111-111-1-1111-1
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111111-111-1111-1-1-111-1-1-1-11-1-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-11111111-11-1-111-111-1
χ172222222-222-22-200-2-220-200-2222-2-200000-20000000000200000000
χ182222222-222-22-200-2-220-200-2-2-22220000020000000000-200000000
χ192222222-222-22-200-2-2-20200222-22200000-20000000000-200000000
χ202222222-222-22-200-2-2-202002-2-2-2-2-20000020000000000200000000
χ21222222-22-2-22-2-222-22020-2-20000000000002-2000000000002-20000
χ22222222-22-2-22-2-222-22020-2-2000000000000-2200000000000-220000
χ23222222-22-2-22-2-2-2-2-220-20220000000000002-200000000000-220000
χ24222222-22-2-22-2-2-2-2-220-2022000000000000-22000000000002-20000
χ252222-2-222-222-2-2222-20-202-2000000000000002000-200-2000002000
χ262222-2-222-222-2-2222-20-202-200000000000000-2000200200000-2000
χ272222-2-222-222-2-2-2-22-2020-22000000000000002000-200200000-2000
χ282222-2-222-222-2-2-2-22-2020-2200000000000000-2000200-2000002000
χ292222-2-2-222-222222-2-22-2-2-22200-2000000-200002000000000000000
χ302222-2-2-222-222222-2-2-2-22-22-200200000020000-2000000000000000
χ312222-2-2-222-2222-2-2-2-222-22-2200-200000020000-2000000000000000
χ322222-2-2-222-2222-2-2-2-2-2222-2-2002000000-200002000000000000000
χ332222-2-2-2-22-2-22-2002220200-200-20000000000002-2000002-2000000
χ342222-2-2-2-22-2-22-2002220200-200-2000000000000-2200000-22000000
χ352222-2-2-2-22-2-22-20022-20-20020020000000000002-200000-22000000
χ362222-2-2-2-22-2-22-20022-20-2002002000000000000-22000002-2000000
χ37444444-4-4-4-4-4-44004-4000000000000000000000000000000000000
χ384444-4-44-4-44-4-4400-44000000000000000000000000000000000000
χ394-44-4000400-4004i−4i00000000000002i2i−2i−2i0000000002-20000000000
χ404-44-4000400-4004i−4i0000000000000−2i−2i2i2i000000000-220000000000
χ414-44-4000400-400−4i4i00000000000002i2i−2i−2i000000000-220000000000
χ424-44-4000400-400−4i4i0000000000000−2i−2i2i2i0000000002-20000000000
χ434-4-444-4404-40-4000000000004i−4i0000000000000000000000000000
χ444-4-444-4404-40-400000000000−4i4i0000000000000000000000000000
χ454-4-444-4-40-4404000000000000000022−2222−22000000000000000000000
χ464-4-444-4-40-44040000000000000000−2222−2222000000000000000000000
χ474-4-44-4440-4-4040000000000000000000000000000000000000022−220
χ484-4-44-4440-4-40400000000000000000000000000000000000000−22220
χ494-4-44-44-40440-4000000000000004-40000000000000000000000000
χ504-4-44-44-40440-400000000000000-440000000000000000000000000
χ5188-8-80000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5288-8-8000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ538-88-8000-8008000000000000000000000000000000000000000000

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