Finite Group Databasebeta

← Group #251077

Character table — Group #251077

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444444444222444444888888224444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11-11111-1-1-1-1-11-111-1-1-1-1-1-1
χ3111111111111111111111-1-1111-1-111111-11-1-1-1-1-1-111-1-1-1-1-1-1-1111
χ4111111111111111111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-11-1-1111-1-1-1
χ51111111111111111111-1-1111-1-1-1-11111-1-1-111111-111-1-1-1-111-1-1-1-1
χ61111111111111111111-1-1111-1-1-1-1-1-1-1-1-11-1111-1-11-1-1-11-1-1-1-11111
χ71111111111111111111-1-1-1-11-1-1111111-11-1-1-1-1-1-11111111-1-11-1-1-1
χ81111111111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-11111-1111
χ91111111111111-1-111-1-11111-111111111-1-1-11-1-1-1-1-1-1-111-1-111111-1
χ101111111111111-1-111-1-11111-11111-1-1-1-1-11-11-1-1111111-1-1-1-1-1-1-1-11
χ111111111111111-1-111-1-111-1-1-111-1-11111-11-1-111111-1-1-1-111-1-1-111-1
χ121111111111111-1-111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-111-1111111-1-11
χ131111111111111-1-111-1-1-1-111-1-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-11
χ141111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11-111-1-111-111-1111-1-1111-1
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111111-11-11111-1-1-111-1-1-1-11-1-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1111-111-1-11111-1-1-111-111-1
χ1722222222-222-2-200-2-2002-22202-2220000000-20000000-2000000000
χ1822222222-222-2-200-2-2002-2-2-202-2-2-20000000200000002000000000
χ1922222222-222-2-200-2-200-22220-22-2-20000000-200000002000000000
χ2022222222-222-2-200-2-200-22-2-20-2222000000020000000-2000000000
χ21222222-2-22-2-22-222-22-2-200002000000000000002-200000002-20000
χ22222222-2-22-2-22-222-22-2-20000200000000000000-220000000-220000
χ23222222-2-22-2-22-2-2-2-22220000-2000000000000002-20000000-220000
χ24222222-2-22-2-22-2-2-2-22220000-200000000000000-2200000002-20000
χ252222-2-22-222-22-2222-22-20000-20000000002000000-2000-200002000
χ262222-2-22-222-22-2222-22-20000-2000000000-2000000200020000-2000
χ272222-2-22-222-22-2-2-22-2-22000020000000002000000-200020000-2000
χ282222-2-22-222-22-2-2-22-2-2200002000000000-20000002000-200002000
χ292222-2-2-222-222222-2-2-222-200-2-22000000-202000000000000000000
χ302222-2-2-222-222222-2-2-22-2200-22-200000020-2000000000000000000
χ312222-2-2-222-2222-2-2-2-22-22-2002-2200000020-2000000000000000000
χ322222-2-2-222-2222-2-2-2-22-2-220022-2000000-202000000000000000000
χ332222-2-2-22-2-22-2-200220022000-2-200000000002-200000002-2000000
χ342222-2-2-22-2-22-2-200220022000-2-20000000000-220000000-22000000
χ352222-2-2-22-2-22-2-2002200-2-20002200000000002-20000000-22000000
χ362222-2-2-22-2-22-2-2002200-2-2000220000000000-2200000002-2000000
χ37444444-4-4-4-4-4-44004-4000000000000000000000000000000000000
χ384444-4-44-4-44-4-4400-44000000000000000000000000000000000000
χ394-44-40000400-404i−4i000000000000022-2-20000000002i−2i0000000000
χ404-44-40000400-404i−4i0000000000000-2-222000000000−2i2i0000000000
χ414-44-40000400-40−4i4i000000000000022-2-2000000000−2i2i0000000000
χ424-44-40000400-40−4i4i0000000000000-2-2220000000002i−2i0000000000
χ434-4-444-44-40-440000000000000000000000000000000000000002i2−2i20
χ444-4-444-44-40-44000000000000000000000000000000000000000−2i22i20
χ454-4-444-4-4404-40000000000000004i−4i0000000000000000000000000
χ464-4-444-4-4404-4000000000000000−4i4i0000000000000000000000000
χ474-4-44-44440-4-400000000004i−4i000000000000000000000000000000
χ484-4-44-44440-4-40000000000−4i4i000000000000000000000000000000
χ494-4-44-44-4-40440000000000000000022−2222−22000000000000000000000
χ504-4-44-44-4-404400000000000000000−2222−2222000000000000000000000
χ5188-8-800000000000000000000000022−22−2222000000000000000000000
χ5288-8-8000000000000000000000000−222222−22000000000000000000000
χ538-88-80000-800800000000000000000000000000000000000000000

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