Finite Group Databasebeta

← Group #251146

Character table — Group #251146

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444444444222444444888888224444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111-1111-1-1-1-1111-1-1-1-1-1-1
χ31111111111111111111-1-111-11-1-1-11111111-1-111-1-111-1-1-1-111-1-1-1-1
χ41111111111111111111-1-111-11-1-1-1-1-1-1-1-1-11-1111-11-1-11-1-1-1-1-11111
χ511111111111111111-1-11111111-1-11111-1-1-11-1-1-11-111-1-1-1-1-1-1-1111
χ611111111111111111-1-11111111-1-1-1-1-1-111-111-1-111-1-11-1-1-1111-1-1-1
χ711111111111111111-1-1-1-111-11-1111111-1-1-1-11-1-1-11111111-1-11-1-1-1
χ811111111111111111-1-1-1-111-11-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1111
χ91111111111111-1-1111111-1-11-11111111-1-11-1-1-1-1-1-1-1-111-1-111111-1
χ101111111111111-1-1111111-1-11-1111-1-1-1-1111-11-1-1-1111-11-1-1-1-1-1-1-11
χ111111111111111-1-11111-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-1-1-11111-1-1-11
χ121111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1111-111-1-1111-1
χ131111111111111-1-111-1-111-1-11-11-1-1111111-1-1111-11-1-1-1-111-1-1-111-1
χ141111111111111-1-111-1-111-1-11-11-1-1-1-1-1-1-1-1-1-1-111-1-1111-111111-1-11
χ151111111111111-1-111-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-111-1-1-1-11-1-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-11-1-111-111-1
χ1722222222-222-2-200-2-2222200-20-222000000-2000000000-200000000
χ1822222222-222-2-200-2-222-2-200202-2-2000000-2000000000200000000
χ1922222222-222-2-200-2-2-2-22200-20-2-2-20000002000000000200000000
χ2022222222-222-2-200-2-2-2-2-2-200202220000002000000000-200000000
χ21222222-2-22-2-22-2222-20000-2-20200000002-200000000000002-20000
χ22222222-2-22-2-22-2222-20000-2-2020000000-220000000000000-220000
χ23222222-2-22-2-22-2-2-22-20000220-200000002-20000000000000-220000
χ24222222-2-22-2-22-2-2-22-20000220-20000000-2200000000000002-20000
χ252222-2-22-222-22-222-2200002-20-2000000000002000-200-2000002000
χ262222-2-22-222-22-222-2200002-20-200000000000-2000200200000-2000
χ272222-2-22-222-22-2-2-2-220000-2202000000000002000-200200000-2000
χ282222-2-22-222-22-2-2-2-220000-220200000000000-2000200-2000002000
χ292222-2-2-222-222222-2-2002-2-222-2-2000000000-200020000000000000
χ302222-2-2-222-222222-2-200-22-22-2-220000000002000-20000000000000
χ312222-2-2-222-2222-2-2-2-2002-22-222-20000000002000-20000000000000
χ322222-2-2-222-2222-2-2-2-200-222-2-222000000000-200020000000000000
χ332222-2-2-22-2-22-2-20022002-200-202000000000002-20000002-2000000
χ342222-2-2-22-2-22-2-20022002-200-20200000000000-22000000-22000000
χ352222-2-2-22-2-22-2-2002200-220020-2000000000002-2000000-22000000
χ362222-2-2-22-2-22-2-2002200-220020-200000000000-220000002-2000000
χ37444444-4-4-4-4-4-4400-44000000000000000000000000000000000000
χ384444-4-44-4-44-4-44004-4000000000000000000000000000000000000
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
χ4344-4-4-44440-4-40000004-40000000000000000000000000000000000
χ4444-4-4-44440-4-4000000-440000000000000000000000000000000000
χ4544-4-4-44-4-4044000000000000000002i22i2−2i2−2i2000000000000000000000
χ4644-4-4-44-4-404400000000000000000−2i2−2i22i22i2000000000000000000000
χ474-44-40000400-404i−4i00000000000002i−2i2i−2i0000000002-20000000000
χ484-44-40000400-404i−4i0000000000000−2i2i−2i2i000000000-220000000000
χ494-44-40000400-40−4i4i00000000000002i−2i2i−2i000000000-220000000000
χ504-44-40000400-40−4i4i0000000000000−2i2i−2i2i0000000002-20000000000
χ518-88-80000-800800000000000000000000000000000000000000000
χ528-8-8800000000000000000000000022−22−2222000000000000000000000
χ538-8-88000000000000000000000000−222222−22000000000000000000000

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