Finite Group Databasebeta

← Group #175478

Character table — Group #175478

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444222244444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111-1-1111-1-1-1-1-1111-111-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1111-1-1111-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-11-1-1-1-1-11-1-11111-1111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-1-1-11-1-1-1-1-11-1-111-1-1-11-1-11111-1-1-1-11111
χ9111111111-1-1-1-1-1-1111111111-1-1-1-1-1-111-11-1111-1-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-1-1-1111111111-1-1-1-1-1-111-11-1-1-11-111-1-111-1-111-1-111
χ11111111111-1-1-1-1-1-11111111-1-1-1-1-1111-11-1-1111-11-1-111-1-1-1-111-1-111
χ12111111111-1-1-1-1-1-11111111-1-1-1-1-1111-11-1-11-1-1-1111-1-11111-1-111-1-1
χ13111111111-1-1-1-1-1-111111-1-111-111-1-1-1-1-11-111111-1-1-1-111-1-11111-1-1
χ14111111111-1-1-1-1-1-111111-1-111-111-1-1-1-1-11-11-1-1111111-1-111-1-1-1-111
χ15111111111-1-1-1-1-1-111111-1-1-1-1-1111111-111-111-1-1-1-1-1-11111-1-1-1-111
χ16111111111-1-1-1-1-1-111111-1-1-1-1-1111111-111-1-1-1-1-11111-1-1-1-11111-1-1
χ1722222222222-2-222-2-2-2-220022-20022-20000000-2000000000000000
χ1822222222222-2-222-2-2-2-2200-2-2-200-2-2200000002000000000000000
χ19222222222-2-222-2-2-2-2-2-220022200-2-220000000-2000000000000000
χ20222222222-2-222-2-2-2-2-2-2200-2-220022-200000002000000000000000
χ2122222222-22222-2-222-2-2-22200-2-2-20000-2200000000000000000000
χ2222222222-22222-2-222-2-2-2-2-200-22200002-200000000000000000000
χ2322222222-222-2-2-2-2-2-222-20000200000200-2-2000200000000000000
χ2422222222-222-2-2-2-2-2-222-20000200000-20022000-200000000000000
χ2522222222-2-2-22222-2-222-20000-200000200-22000-200000000000000
χ2622222222-2-2-22222-2-222-20000-200000-2002-2000200000000000000
χ2722222222-2-2-2-2-22222-2-2-222002220000-2-200000000000000000000
χ2822222222-2-2-2-2-22222-2-2-2-2-2002-2-200002200000000000000000000
χ294444-4-4-4-440000000000-4004-400000000000000000000000000000
χ304444-4-4-4-440000000000-400-4400000000000000000000000000000
χ314444-4-4-4-4-40000000000400000004i−4i000000000000000000000000
χ324444-4-4-4-4-4000000000040000000−4i4i000000000000000000000000
χ3344-4-4-444-404i−4i0000000000000000000000002-2002i−2i000000000000
χ3444-4-4-444-404i−4i000000000000000000000000-2200−2i2i000000000000
χ3544-4-4-444-40−4i4i0000000000000000000000002-200−2i2i000000000000
χ3644-4-4-444-40−4i4i000000000000000000000000-22002i−2i000000000000
χ374-44-444-4-4000004i−4i0000000000000000000000000000002-22i−2i0000
χ384-44-444-4-4000004i−4i000000000000000000000000000000-22−2i2i0000
χ394-44-444-4-400000−4i4i0000000000000000000000000000002-2−2i2i0000
χ404-44-444-4-400000−4i4i000000000000000000000000000000-222i−2i0000
χ414-44-4-4-44400000004-4000000004-400000000000000000000000000
χ424-44-4-4-44400000004-400000000-4400000000000000000000000000
χ434-44-4-4-4440000000-440004-40000000000000000000000000000000
χ444-44-4-4-4440000000-44000-440000000000000000000000000000000
χ454-4-444-44-40004-400000000000000000000000000002i−2i2i−2i00000000
χ464-4-444-44-40004-40000000000000000000000000000−2i2i−2i2i00000000
χ474-4-444-44-4000-4400000000000000000000000000002i−2i−2i2i00000000
χ484-4-444-44-4000-440000000000000000000000000000−2i2i2i−2i00000000
χ494-4-44-44-440000000004-400000000000000000000000000000022−2200
χ504-4-44-44-440000000004-4000000000000000000000000000000−222200
χ514-4-44-44-44000000000-440000000000000000000000000000000022−22
χ524-4-44-44-44000000000-4400000000000000000000000000000000−2222
χ5388-8-88-8-88000000000000000000000000000000000000000000000

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