Finite Group Databasebeta

← Group #175477

Character table — Group #175477

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444222244444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-11-1-1-11-1-111-111-1-1-1-1-1-1-1-11111
χ41111111111111111111111-1-1111-1-11-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111-1-1111-1-111-1-11-1-11-111-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1111-1-111-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-11-1-1-1-1-11-11-1-1111111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-1-1-11-1-1-1-1-11-11-1-11-1-11-1-11111-1-1-1-11111
χ9111111111-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-111
χ11111111111-1-1-1-1-1-11111111-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ12111111111-1-1-1-1-1-11111111-1-1-1-1-111-1-1-1-1111-1-111111-1-111-1-1-1-111
χ13111111111-1-1-1-1-1-111111-1-111-111-1-11-11-1-1-11111-1-111-1-1-1-111-1-111
χ14111111111-1-1-1-1-1-111111-1-111-111-1-11-11-1-1-11-1-1111-1-11111-1-111-1-1
χ15111111111-1-1-1-1-1-111111-1-1-1-1-1111111-11-11-111-1-1-1-1-11111-1-1-1-111
χ16111111111-1-1-1-1-1-111111-1-1-1-1-1111111-11-11-1-1-1-11111-1-1-1-11111-1-1
χ1722222222222-2-2-2-2-2-2-2-2222002-2-2002000-20000000000000000000
χ1822222222222-2-2-2-2-2-2-2-22-2-20022200-200020000000000000000000
χ19222222222-2-22222-2-2-2-222200-22200-2000-20000000000000000000
χ20222222222-2-22222-2-2-2-22-2-200-2-2-200200020000000000000000000
χ2122222222-22222-2-222-2-2-20000-20000020-200-200200000000000000
χ2222222222-22222-2-222-2-2-20000-200000-20200200-200000000000000
χ2322222222-222-2-222-2-222-20022-200-2-200-2002000000000000000000
χ2422222222-222-2-222-2-222-200-2-2-2002200200-2000000000000000000
χ2522222222-2-2-222-2-2-2-222-200222002200-200-2000000000000000000
χ2622222222-2-2-222-2-2-2-222-200-2-2200-2-2002002000000000000000000
χ2722222222-2-2-2-2-22222-2-2-2000020000020-200200-200000000000000
χ2822222222-2-2-2-2-22222-2-2-20000200000-20200-200200000000000000
χ29444-4-4-4-44000004i−4i0000000000000000000002i−2i02-2000000000000
χ30444-4-4-4-44000004i−4i000000000000000000000−2i2i0-22000000000000
χ31444-4-4-4-4400000−4i4i0000000000000000000002i−2i0-22000000000000
χ32444-4-4-4-4400000−4i4i000000000000000000000−2i2i02-2000000000000
χ3344-444-4-4-440000000000-44-40000000000000000000000000000000
χ3444-444-4-4-440000000000-4-440000000000000000000000000000000
χ3544-444-4-4-4-400000000004000004i−4i00000000000000000000000000
χ3644-444-4-4-4-40000000000400000−4i4i00000000000000000000000000
χ374-444-44-4-400000004-400000000000000000000000000000000002i2−2i2
χ384-444-44-4-400000004-40000000000000000000000000000000000−2i22i2
χ394-444-44-4-40000000-44000000000000000000000000000000002i2−2i200
χ404-444-44-4-40000000-4400000000000000000000000000000000−2i22i200
χ414-44-44-44-40004i−4i000000000000000000000000000000002-22i−2i0000
χ424-44-44-44-40004i−4i00000000000000000000000000000000-22−2i2i0000
χ434-44-44-44-4000−4i4i000000000000000000000000000000002-2−2i2i0000
χ444-44-44-44-4000−4i4i00000000000000000000000000000000-222i−2i0000
χ454-4-44-4-44404-40000000000000000000000000000002-22-200000000
χ464-4-44-4-44404-4000000000000000000000000000000-22-2200000000
χ474-4-44-4-4440-440000000000000000000000000000002-2-2200000000
χ484-4-44-4-4440-44000000000000000000000000000000-222-200000000
χ494-4-4-444-440000000004-4000000004-4000000000000000000000000
χ504-4-4-444-440000000004-400000000-44000000000000000000000000
χ514-4-4-444-44000000000-440004-400000000000000000000000000000
χ524-4-4-444-44000000000-44000-4400000000000000000000000000000
χ5388-8-8-888-8000000000000000000000000000000000000000000000

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