Finite Group Databasebeta

← Group #175967

Character table — Group #175967

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444444444422244444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1111-1-11-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-11111
χ51111111111111111111-1-11-1-11111-1-1-1111-1-11-11111-1-1-1-1-1-1-1-1
χ61111111111111111111-1-11-1-111-1-111-111-11-1-11-1-1-1-1-1-1-1-11111
χ71111111111111111111-1-11-1-1-1-111-1-1-1-1-11-1-11-1-1-1-1-111111111
χ81111111111111111111-1-11-1-1-1-1-1-111-1-1-1-11-1-1111111111-1-1-1-1
χ9111111111-1-11-1-11111-111-1-1-1111-11-1-1-1-1-1111-111-1-111-1-111-1-1
χ10111111111-1-11-1-11111-111-1-1-111-11-11-1-1-11-11-11-1-11111-1-1-1-111
χ11111111111-1-11-1-11111-111-1-1-1-1-11-11-1-111-1111-1-1-111-1-111-1-111
χ12111111111-1-11-1-11111-111-1-1-1-1-1-11-11-1111-11-1111-1-1-1-11111-1-1
χ13111111111-1-11-1-11111-1-1-1-111111-1-111-1-1-1-1-11111-1-1-1-111-1-111
χ14111111111-1-11-1-11111-1-1-1-11111-111-11-1-111-1-1-1-1-111-1-11111-1-1
χ15111111111-1-11-1-11111-1-1-1-111-1-11-1-11111-1-1-111-1-11111-1-111-1-1
χ16111111111-1-11-1-11111-1-1-1-111-1-1-111-111111-1-1-111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-22-2222-222000000-20000-200000000000000
χ1822222222222-2-2-2-2-22-22-2-2-2-2-200000020000200000000000000
χ19222222222-2-2-222-2-22-2-2222-2-200000020000-200000000000000
χ20222222222-2-2-222-2-22-2-2-2-2222000000-20000200000000000000
χ2122222222-2222-2-2-2-2-22-2002000000220000-200-2000000000000
χ2222222222-2222-2-2-2-2-22-2002000000-2-200002002000000000000
χ2322222222-222-22222-2-2-200-200002200000-200-20000000000000
χ2422222222-222-22222-2-2-200-20000-2-20000020020000000000000
χ2522222222-2-2-2222-2-2-22200-20000002-20000-2002000000000000
χ2622222222-2-2-2222-2-2-22200-2000000-220000200-2000000000000
χ2722222222-2-2-2-2-2-222-2-2200200002-200000200-20000000000000
χ2822222222-2-2-2-2-2-222-2-220020000-2200000-20020000000000000
χ2944-4-444-4-404i−4i00000000000002-2000002i−2i00000000000000000
χ3044-4-444-4-404i−4i0000000000000-2200000−2i2i00000000000000000
χ3144-4-444-4-40−4i4i00000000000002-200000−2i2i00000000000000000
χ3244-4-444-4-40−4i4i0000000000000-22000002i−2i00000000000000000
χ3344-4-4-4-44440000000-4004i−4i00000000000000000000000000000
χ3444-4-4-4-44440000000-400−4i4i00000000000000000000000000000
χ3544-4-4-4-444-400000004000004-400000000000000000000000000
χ3644-4-4-4-444-40000000400000-4400000000000000000000000000
χ374-44-44-44-40000004-400000000000000000000000000002i2−2i20000
χ384-44-44-44-40000004-40000000000000000000000000000−2i22i20000
χ394-44-44-44-4000000-44000000000000000000000000002i2−2i2000000
χ404-44-44-44-4000000-4400000000000000000000000000−2i22i2000000
χ414-44-4-44-44000400000-400000000000000000000002i2−2i200000000
χ424-44-4-44-44000400000-40000000000000000000000−2i22i200000000
χ434-44-4-44-44000-40000040000000000000000000022−220000000000
χ444-44-4-44-44000-400000400000000000000000000−22220000000000
χ454-4-44-444-400004-4000000000000000000000000000000002i−2i2i−2i
χ464-4-44-444-400004-400000000000000000000000000000000−2i2i−2i2i
χ474-4-44-444-40000-44000000000000000000000000000000002i−2i−2i2i
χ484-4-44-444-40000-4400000000000000000000000000000000−2i2i2i−2i
χ498888-8-8-8-8000000000000000000000000000000000000000000
χ508-8-888-8-88000000000000000000000000000000000000000000

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