Finite Group Databasebeta

← Group #251154

Character table — Group #251154

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444444444244444444888888224444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111-1111-1-1-1-1111-1-1-1-1-1-1
χ31111111111111111111-1-111111-1-11111-1-11-1-11-1-1-111-1-1-1-1-1-1-1111
χ41111111111111111111-1-111111-1-1-1-1-1-1111-111-1-11-1-11-1-1-1111-1-1-1
χ511111111111111111-1-1111-111-1-1-1111111-11-1-111-111-1-1-1-111-1-1-1-1
χ611111111111111111-1-1111-111-1-1-1-1-1-1-1-1-1-111-1111-1-11-1-1-1-1-11111
χ711111111111111111-1-1-1-11-111-1111111-1-1-1-11-1-1-11111111-1-11-1-1-1
χ811111111111111111-1-1-1-11-111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1111
χ91111111111111-1-1111111-11-1-11111111-1-1-11-1-1-1-1-1-1-111-1-111111-1
χ101111111111111-1-1111111-11-1-1111-1-1-1-111-111-1-1-1111-11-1-1-1-1-1-1-11
χ111111111111111-1-11111-1-1-11-1-11-1-1111111-1-11-1111-1-1-1-111-1-1-111-1
χ121111111111111-1-11111-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1111-111111-1-11
χ131111111111111-1-111-1-111-1-1-1-1-1-1-11111-1-11111-1-11-1-1-1-11111-1-1-11
χ141111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1111-111-1-1111-1
χ151111111111111-1-111-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-111-1-1-1-11-1-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111111-11-1-111-111-1
χ1722222222-222-2-200-2-222220-200-2220000000-200000000-200000000
χ1822222222-222-2-200-2-222-2-20-200-2-2-20000000200000000200000000
χ1922222222-222-2-200-2-2-2-22202002-2-20000000-200000000200000000
χ2022222222-222-2-200-2-2-2-2-2-202002220000000200000000-200000000
χ21222222-2-22-2-22-222-22000020-2-200000002-200000000000002-20000
χ22222222-2-22-2-22-222-22000020-2-20000000-220000000000000-220000
χ23222222-2-22-2-22-2-2-2-220000-202200000002-20000000000000-220000
χ24222222-2-22-2-22-2-2-2-220000-20220000000-2200000000000002-20000
χ252222-2-22-222-22-2222-20000-202-2000000000002000-200200000-2000
χ262222-2-22-222-22-2222-20000-202-200000000000-2000200-2000002000
χ272222-2-22-222-22-2-2-22-2000020-22000000000002000-200-2000002000
χ282222-2-22-222-22-2-2-22-2000020-2200000000000-2000200200000-2000
χ292222-2-2-222-222222-2-22-200-2-2-22200000000200-2000000000000000
χ302222-2-2-222-222222-2-2-2200-22-22-200000000-2002000000000000000
χ312222-2-2-222-2222-2-2-2-22-2002-22-2200000000-2002000000000000000
χ322222-2-2-222-2222-2-2-2-2-2200222-2-200000000200-2000000000000000
χ332222-2-2-22-2-22-2-200222-2000200-20000000000002-2000002-2000000
χ342222-2-2-22-2-22-2-200222-2000200-2000000000000-2200000-22000000
χ352222-2-2-22-2-22-2-20022-22000-20020000000000002-200000-22000000
χ362222-2-2-22-2-22-2-20022-22000-2002000000000000-22000002-2000000
χ37444444-4-4-4-4-4-44004-4000000000000000000000000000000000000
χ384444-4-44-4-44-4-4400-44000000000000000000000000000000000000
χ3944-4-44-44-40-4400000000000000000000000000000000000000022−220
χ4044-4-44-44-40-44000000000000000000000000000000000000000−22220
χ4144-4-44-4-4404-40000000000000004-40000000000000000000000000
χ4244-4-44-4-4404-4000000000000000-440000000000000000000000000
χ4344-4-4-44440-4-4000000004-400000000000000000000000000000000
χ4444-4-4-44440-4-400000000-4400000000000000000000000000000000
χ4544-4-4-44-4-4044000000000000000002i22i2−2i2−2i2000000000000000000000
χ4644-4-4-44-4-404400000000000000000−2i2−2i22i22i2000000000000000000000
χ474-4-440000400-404i−4i00000000000002-22-20000000002i−2i0000000000
χ484-4-440000400-404i−4i0000000000000-22-22000000000−2i2i0000000000
χ494-4-440000400-40−4i4i00000000000002-22-2000000000−2i2i0000000000
χ504-4-440000400-40−4i4i0000000000000-22-220000000002i−2i0000000000
χ518-88-80000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ528-88-8000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ538-8-880000-800800000000000000000000000000000000000000000

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