Finite Group Databasebeta

← Group #176105

Character table — Group #176105

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444424444424444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11-1-1-111-1-1111-111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11-1-1-111-1-1-1-11-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-11-1-1-1-11111-1111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-11-1-1-1-111-1-1-11-1-111111111-1-1-1-1
χ9111111111-1-111-1-1111-1-111-1-1111-11-1-1-111-11-1-111-1-111-1-111-1-1
χ10111111111-1-111-1-1111-1-111-1-1111-11-1-1-1-1-1-1111-1-111-1-111-1-111
χ11111111111-1-111-1-1111-1-111-1-1-1-11-1-1111111-1-1-111-1-1-1-111-1-111
χ12111111111-1-111-1-1111-1-111-1-1-1-11-1-1111-1-11-111-1-11111-1-111-1-1
χ13111111111-1-111-1-1111-1-1-1-1111-1-111-11111-1-1-1-1-1-11111-1-1-1-111
χ14111111111-1-111-1-1111-1-1-1-1111-1-111-111-1-1-1-11111-1-1-1-11111-1-1
χ15111111111-1-111-1-1111-1-1-1-111-11-11-11-1-11111-1-1-1-111-1-11111-1-1
χ16111111111-1-111-1-1111-1-1-1-111-11-11-11-1-1-1-1111111-1-111-1-1-1-111
χ1722222222222-2-2-2-22-2-22-200002000-220000-2000000000000000
χ1822222222222-2-2-2-22-2-22-20000-20002-200002000000000000000
χ19222222222-2-2-2-2222-2-2-2200002000-2-200002000000000000000
χ20222222222-2-2-2-2222-2-2-220000-2000220000-2000000000000000
χ2122222222-2222-222-22-2-2-200000200002-2000-200000000000000
χ2222222222-2222-222-22-2-2-200000-20000-22000200000000000000
χ2322222222-222-22-2-2-2-22-22222200-2-20000000000000000000000
χ2422222222-222-22-2-2-2-22-22-2-2-2-200220000000000000000000000
χ2522222222-2-2-22-2-2-2-22-2220000020000-22000-200000000000000
χ2622222222-2-2-22-2-2-2-22-22200000-200002-2000200000000000000
χ2722222222-2-2-2-2222-2-222-222-2-200-220000000000000000000000
χ2822222222-2-2-2-2222-2-222-2-2-222002-20000000000000000000000
χ29444-4-4-4-444000000-40000000000000000000000000000000022−22
χ30444-4-4-4-444000000-400000000000000000000000000000000−2222
χ31444-4-4-4-44-400000040000000000000000000000000000002i2−2i200
χ32444-4-4-4-44-40000004000000000000000000000000000000−2i22i200
χ3344-444-4-4-4000040000-400004-400000000000000000000000000
χ3444-444-4-4-4000040000-40000-4400000000000000000000000000
χ3544-444-4-4-40000-400004004i−4i0000000000000000000000000000
χ3644-444-4-4-40000-40000400−4i4i0000000000000000000000000000
χ374-444-44-4-4000004i−4i0000000000000000000000000002-22i−2i0000
χ384-444-44-4-4000004i−4i000000000000000000000000000-22−2i2i0000
χ394-444-44-4-400000−4i4i0000000000000000000000000002-2−2i2i0000
χ404-444-44-4-400000−4i4i000000000000000000000000000-222i−2i0000
χ414-44-44-44-404-40000000000000000000002i−2i002i−2i000000000000
χ424-44-44-44-404-4000000000000000000000−2i2i00−2i2i000000000000
χ434-44-44-44-40-440000000000000000000002i−2i00−2i2i000000000000
χ444-44-44-44-40-44000000000000000000000−2i2i002i−2i000000000000
χ454-4-44-4-44400040000-4000000000000000000000002i2−2i200000000
χ464-4-44-4-44400040000-400000000000000000000000−2i22i200000000
χ474-4-44-4-444000-40000400000000000000000000022−220000000000
χ484-4-44-4-444000-400004000000000000000000000−22220000000000
χ4988-8-8-888-8000000000000000000000000000000000000000000
χ508-8-8-888-88000000000000000000000000000000000000000000

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