Finite Group Databasebeta

← Group #177923

Character table — Group #177923

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444422224422444444444444888888888888
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
χ5111111111111111111-1-1-1-1111-1-1-111-1-1111-111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1111-1-1-111-1-1-1-11-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-11-1-1-1-11111-1111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-11-1-1-1-111-1-1-11-1-111111111-1-1-1-1
χ9111111111-1-11-1-1111111-1-1-1-1111-11-1-1-111-11-1-111-1-111-1-111-1-1
χ10111111111-1-11-1-1111111-1-1-1-1111-11-1-1-1-1-1-1111-1-111-1-111-1-111
χ11111111111-1-11-1-1111111-1-1-1-1-1-11-1-1111111-1-1-111-1-1-1-111-1-111
χ12111111111-1-11-1-1111111-1-1-1-1-1-11-1-1111-1-11-111-1-11111-1-111-1-1
χ13111111111-1-11-1-11111-1-111-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111
χ14111111111-1-11-1-11111-1-111-1-11-1-111-111-1-1-1-11111-1-1-1-11111-1-1
χ15111111111-1-11-1-11111-1-111-1-1-11-11-11-1-11111-1-1-1-111-1-11111-1-1
χ16111111111-1-11-1-11111-1-111-1-1-11-11-11-1-1-1-1111111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-22-200002-22000-2-200002000000000000000
χ1822222222222-2-2-2-2-22-200002-2-2000220000-2000000000000000
χ19222222222-2-2-222-2-22-20000-222000-220000-2000000000000000
χ20222222222-2-2-222-2-22-20000-22-20002-200002000000000000000
χ2122222222-2222-2-2-2-2-220000-220200002-2000-200000000000000
χ2222222222-2222-2-2-2-2-220000-220-20000-22000200000000000000
χ2322222222-222-22222-2-222-2-2-2-200-220000000000000000000000
χ2422222222-222-22222-2-2-2-222-2-2002-20000000000000000000000
χ2522222222-2-2-2222-2-2-2200002-2020000-22000-200000000000000
χ2622222222-2-2-2222-2-2-2200002-20-200002-2000200000000000000
χ2722222222-2-2-2-2-2-222-2-222222200-2-20000000000000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2-2-22200220000000000000000000000
χ2944-444-4-4-404i−4i0000000000000000000002-2002i−2i000000000000
χ3044-444-4-4-404i−4i000000000000000000000-2200−2i2i000000000000
χ3144-444-4-4-40−4i4i0000000000000000000002-200−2i2i000000000000
χ3244-444-4-4-40−4i4i000000000000000000000-22002i−2i000000000000
χ3344-4-4-44-4440000000-4000000000000000000000000000002i2−2i200
χ3444-4-4-44-4440000000-400000000000000000000000000000−2i22i200
χ3544-4-4-44-44-400000004000000000000000000000000000000022−22
χ3644-4-4-44-44-4000000040000000000000000000000000000000−2222
χ374-444-44-4-400004-40000000000000000000000002i−2i2i−2i00000000
χ384-444-44-4-400004-4000000000000000000000000−2i2i−2i2i00000000
χ394-444-44-4-40000-440000000000000000000000002i−2i−2i2i00000000
χ404-444-44-4-40000-44000000000000000000000000−2i2i2i−2i00000000
χ414-4-44-4-4440000004-400004-40000000000000000000000000000
χ424-4-44-4-4440000004-40000-440000000000000000000000000000
χ434-4-44-4-444000000-44004-4000000000000000000000000000000
χ444-4-44-4-444000000-4400-44000000000000000000000000000000
χ454-4-4-4444-4000400000-4000000000000000000000000002i2−2i20000
χ464-4-4-4444-4000400000-400000000000000000000000000−2i22i20000
χ474-4-4-4444-4000-400000400000000000000000000000022−22000000
χ484-4-4-4444-4000-4000004000000000000000000000000−2222000000
χ49888-8-8-88-8000000000000000000000000000000000000000000
χ508-88-88-8-88000000000000000000000000000000000000000000

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