Finite Group Databasebeta

← Group #178122

Character table — Group #178122

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444422444422444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1111-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-1-11-1-1-11111-1-1-1-11111
χ5111111111111111111-1-11-1-111-11-1-111-111-1-111-1-1-1-1-1-1-1-11111
χ6111111111111111111-1-11-1-111-11-1-111-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111-1-11-1-11-11-11-1-1-1111-11111111-1-1-1-1-1-1-1-1
χ8111111111111111111-1-11-1-11-11-11-1-1-11-1-1-11-1-1-1-1-1-111111111
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
χ11111111111-1-11-1-1111111-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-111
χ12111111111-1-11-1-1111111-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1
χ13111111111-1-11-1-11111-1-1-111-11-111-1-1-11111-1-1-1-1-111-1-11111-1-1
χ14111111111-1-11-1-11111-1-1-111-11-111-1-1-11-1-11-11111-1-111-1-1-1-111
χ15111111111-1-11-1-11111-1-1-111-1-11-1-1-111-11111-1-111-1-1-1-111-1-111
χ16111111111-1-11-1-11111-1-1-111-1-11-1-1-111-1-1-11111-1-11111-1-111-1-1
χ1722222222222-2-2-2-2-22-200200-220-2002-20000000000000000000
χ1822222222222-2-2-2-2-22-200200-2-20200-220000000000000000000
χ19222222222-2-2-222-2-22-200-200220-200-220000000000000000000
χ20222222222-2-2-222-2-22-200-2002-202002-20000000000000000000
χ2122222222-222222-2-2-2222-2-2-2-20000-2000002000000000000000
χ2222222222-222222-2-2-22-2-2-222-20000200000-2000000000000000
χ2322222222-222-2-2-222-2-200-20020202000-2000-200000000000000
χ2422222222-222-2-2-222-2-200-20020-20-20002000200000000000000
χ2522222222-2-2-22-2-2-2-2-222222220000-200000-2000000000000000
χ2622222222-2-2-22-2-2-2-2-22-2-22-2-2200002000002000000000000000
χ2722222222-2-2-2-22222-2-200200-2020-20002000-200000000000000
χ2822222222-2-2-2-22222-2-200200-20-202000-2000200000000000000
χ2944-4-444-4-404i−4i0000000000000000000002-2002i−2i000000000000
χ3044-4-444-4-404i−4i000000000000000000000-2200−2i2i000000000000
χ3144-4-444-4-40−4i4i0000000000000000000002-200−2i2i000000000000
χ3244-4-444-4-40−4i4i000000000000000000000-22002i−2i000000000000
χ3344-4-4-4-44440000000-40000000000000000000002i2−2i20000000000
χ3444-4-4-4-44440000000-4000000000000000000000−2i22i20000000000
χ3544-4-4-4-444-4000000040000000000000000000000022−2200000000
χ3644-4-4-4-444-40000000400000000000000000000000−222200000000
χ374-44-44-44-40000004-4000000000000000000000000000000002i2−2i2
χ384-44-44-44-40000004-400000000000000000000000000000000−2i22i2
χ394-44-44-44-4000000-440000000000000000000000000000002i2−2i200
χ404-44-44-44-4000000-44000000000000000000000000000000−2i22i200
χ414-44-4-44-44000400000-40004i−4i000000000000000000000000000
χ424-44-4-44-44000400000-4000−4i4i000000000000000000000000000
χ434-44-4-44-44000-40000044-4000000000000000000000000000000
χ444-44-4-44-44000-4000004-44000000000000000000000000000000
χ454-4-44-444-400004i−4i00000000000000000000000000002-22i−2i0000
χ464-4-44-444-400004i−4i0000000000000000000000000000-22−2i2i0000
χ474-4-44-444-40000−4i4i00000000000000000000000000002-2−2i2i0000
χ484-4-44-444-40000−4i4i0000000000000000000000000000-222i−2i0000
χ498888-8-8-8-8000000000000000000000000000000000000000000
χ508-8-888-8-88000000000000000000000000000000000000000000

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