Finite Group Databasebeta

← Group #251148

Character table — Group #251148

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444444444244444444888888222444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111-1-11-11-1-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-1-1-1-11-11-111-1-1-1-1-1-1-1111
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-1111-1-1-1
χ511111111111111111-1-111-11-111-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ611111111111111111-1-111-11-111-1-1-1-1-1-1111-1-1-11-11-1-11-1-1-1-1-11111
χ711111111111111111-1-111-11-1-1-1111111-1-1-1-1-1-11-11111111-1-11-1-1-1
χ811111111111111111-1-111-11-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1111
χ91111111111111-1-11111-1-11-11111111111-1-1-1-1-1-1-1-1-1-111-1-111111-1
χ101111111111111-1-11111-1-11-111111-1-1-1-11-1-111-11-1111-11-1-1-1-1-1-1-11
χ111111111111111-1-11111-1-11-11-1-1-1-11111-11111-11-11-1-1-1-111-1-1-111-1
χ121111111111111-1-11111-1-11-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-111111-1-11
χ131111111111111-1-111-1-1-1-1-1-1-111-1-111111-1-1-1-11111-1-1-1-11111-1-1-11
χ141111111111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1111-11-1111-111-1-1111-1
χ151111111111111-1-111-1-1-1-1-1-1-1-1-1111111-111111-11-1-1-111-1-1-1-11-1-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111111-11-1-111-111-1
χ1722222222-222-2-200-2-22200-20-222220000-200000000000-200000000
χ1822222222-222-2-200-2-22200-20-2-2-2-2-20000200000000000200000000
χ1922222222-222-2-200-2-2-2-20020222-2-20000-200000000000200000000
χ2022222222-222-2-200-2-2-2-200202-2-2220000200000000000-200000000
χ21222222-2-22-2-22-222-2200-2-2020000000000002-200000000002-20000
χ22222222-2-22-2-22-222-2200-2-202000000000000-220000000000-220000
χ23222222-2-22-2-22-2-2-2-2200220-20000000000002-20000000000-220000
χ24222222-2-22-2-22-2-2-2-2200220-2000000000000-2200000000002-20000
χ252222-2-22-222-22-2222-2002-20-200000000000000020-200-2000002000
χ262222-2-22-222-22-2222-2002-20-2000000000000000-20200200000-2000
χ272222-2-22-222-22-2-2-22-200-220200000000000000020-200200000-2000
χ282222-2-22-222-22-2-2-22-200-2202000000000000000-20200-2000002000
χ292222-2-2-222-222222-2-22-2-22-2-220000000000000-2020000000000000
χ302222-2-2-222-222222-2-2-22-222-2-2000000000000020-20000000000000
χ312222-2-2-222-2222-2-2-2-22-22-2-222000000000000020-20000000000000
χ322222-2-2-222-2222-2-2-2-2-222-222-20000000000000-2020000000000000
χ332222-2-2-22-2-22-2-200222-20020-20000000002-200000000002-2000000
χ342222-2-2-22-2-22-2-200222-20020-2000000000-220000000000-22000000
χ352222-2-2-22-2-22-2-20022-2200-2020000000002-20000000000-22000000
χ362222-2-2-22-2-22-2-20022-2200-202000000000-2200000000002-2000000
χ37444444-4-4-4-4-4-44004-4000000000000000000000000000000000000
χ384444-4-44-4-44-4-4400-44000000000000000000000000000000000000
χ3944-4-44-4440-4-4000000000000000002222−22−22000000000000000000000
χ4044-4-44-4440-4-400000000000000000−22−222222000000000000000000000
χ4144-4-44-4-4-404400000000000004i−4i000000000000000000000000000
χ4244-4-44-4-4-40440000000000000−4i4i000000000000000000000000000
χ4344-4-4-444-40-440000000000000004i−4i0000000000000000000000000
χ4444-4-4-444-40-44000000000000000−4i4i0000000000000000000000000
χ4544-4-4-44-4404-40000000000000000000000000000000000000002i2−2i20
χ4644-4-4-44-4404-4000000000000000000000000000000000000000−2i22i20
χ474-4-440000400-404-400000000000002i−2i2i−2i0000000002i−2i0000000000
χ484-4-440000400-404-40000000000000−2i2i−2i2i000000000−2i2i0000000000
χ494-4-440000400-40-4400000000000002i−2i2i−2i000000000−2i2i0000000000
χ504-4-440000400-40-440000000000000−2i2i−2i2i0000000002i−2i0000000000
χ518-88-80000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ528-88-8000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ538-8-880000-800800000000000000000000000000000000000000000

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