Finite Group Databasebeta

← Group #175333

Character table — Group #175333

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444224444444222444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-1111-11-1-111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111-1-111-111-1-1-11-1111-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1111-1-111-1-1-1-1-1-11-1-1-11-111111111-1-1-1-1
χ711111111111111111111-1-11-1-1-1-1-1-1111-11-1-1111-11-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-11-1-1-1-1-1-11-1-1-11-1-11-1-1-111111-1-1-1-11111
χ9111111111-1-1-1-1-1-11111111-111-1-1-1-1111-1-11-11-1-11-111-1-111-1-111-1-1
χ10111111111-1-1-1-1-1-11111111-111-1-1-1-11-1-1-1-11-11111-1-1-111-1-111-1-111
χ11111111111-1-1-1-1-1-11111111-1-1-1-1-111-111-1111-1-1-1-1111-1-1-1-111-1-111
χ12111111111-1-1-1-1-1-11111111-1-1-1-1-111-1-1-1-1111-111-11-1-11111-1-111-1-1
χ13111111111-1-1-1-1-1-111111-1-1-11111-1-1-11111-1-1-1-1-111-1-111-1-11111-1-1
χ14111111111-1-1-1-1-1-111111-1-1-11111-1-1-1-1-111-1-1-1111111-1-111-1-1-1-111
χ15111111111-1-1-1-1-1-111111-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-111
χ16111111111-1-1-1-1-1-111111-1-1-1-1-111111-1-11-1-11111-1-111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-2200-2220022000000-2000-20000000000000
χ182222222222222-2-2-2-2-2-2200-2-2-200-2-2000000200020000000000000
χ19222222222-2-2-2-222-2-2-2-220022200-2-20000002000-20000000000000
χ20222222222-2-2-2-222-2-2-2-22002-2-20022000000-200020000000000000
χ2122222222-222-2-22222-2-2-200-20000002000-200-20002000000000000
χ2222222222-222-2-22222-2-2-200-2000000-20002002000-2000000000000
χ2322222222-222-2-2-2-2-2-222-2222002200000-20-2000000000000000000
χ2422222222-222-2-2-2-2-2-222-2-2-2200-2-200000202000000000000000000
χ2522222222-2-2-22222-2-222-222-200-2-20000020-2000000000000000000
χ2622222222-2-2-22222-2-222-2-2-2-2002200000-202000000000000000000
χ2722222222-2-2-222-2-222-2-2-20020000002000200-2000-2000000000000
χ2822222222-2-2-222-2-222-2-2-2002000000-2000-20020002000000000000
χ29444-4-4-4-440004i−4i000000000000000002-2000002i−2i00000000000000
χ30444-4-4-4-440004i−4i00000000000000000-2200000−2i2i00000000000000
χ31444-4-4-4-44000−4i4i000000000000000002-200000−2i2i00000000000000
χ32444-4-4-4-44000−4i4i00000000000000000-22000002i−2i00000000000000
χ3344-44-44-4-400000004-400000000000000000000000000000000002i2−2i2
χ3444-44-44-4-400000004-40000000000000000000000000000000000−2i22i2
χ3544-44-44-4-40000000-44000000000000000000000000000000002i2−2i200
χ3644-44-44-4-40000000-4400000000000000000000000000000000−2i22i200
χ3744-4-44-44-404i−4i00000000000000000000000000000000002-22i−2i0000
χ3844-4-44-44-404i−4i0000000000000000000000000000000000-22−2i2i0000
χ3944-4-44-44-40−4i4i00000000000000000000000000000000002-2−2i2i0000
χ4044-4-44-44-40−4i4i0000000000000000000000000000000000-222i−2i0000
χ414-44-4-444-440000000000-400000004i−4i000000000000000000000000
χ424-44-4-444-440000000000-40000000−4i4i000000000000000000000000
χ434-44-4-444-4-4000000000040004-40000000000000000000000000000
χ444-44-4-444-4-400000000004000-440000000000000000000000000000
χ454-4-44-4-4440000000004-40000004-400000000000000000000000000
χ464-4-44-4-4440000000004-4000000-4400000000000000000000000000
χ474-4-44-4-444000000000-4404-40000000000000000000000000000000
χ484-4-44-4-444000000000-440-440000000000000000000000000000000
χ494-4-4-444-44000004-4000000000000000000000000002-22-200000000
χ504-4-4-444-44000004-400000000000000000000000000-22-2200000000
χ514-4-4-444-4400000-44000000000000000000000000002-2-2200000000
χ524-4-4-444-4400000-4400000000000000000000000000-222-200000000
χ538-8888-8-8-8000000000000000000000000000000000000000000000

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