Finite Group Databasebeta

← Group #7500639

Character table — Group #7500639

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444888888888888881616161611111111222244444444444444448888888888888816161616
order12222222444422224444888888882244444444888844442222222244442222444488888888224444444488884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-11111111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1
χ511111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11-11-111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11-11-1
χ611111111111111-1-1-1-11111111111-1-1-111-1-1-111-1-1-1-1-11-1111111111111111-1-1-1-11111111111-1-1-111-1-1-111-1-1-1-1-11-11
χ711111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-111-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-111-1
χ811111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111-1-111111-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111-1-111111-1-11
χ9111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-11111111-1-1-1-1-11111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-11111111-1-1-1-1-11
χ10111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1
χ11111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-1-1-11111-11111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-1-1-11111-11
χ12111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-11111111-1-111-1-11-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-11111111-1-111-1-11-1
χ13111111111111-1-1-1-111-1-11111-1-1-1-111111-111-1-1-1-111-11-1-1111111111111-1-1-1-111-1-11111-1-1-1-111111-111-1-1-1-111-11-1-1
χ14111111111111-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-1-1-111-1-1111-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-1-1-111-1-1111-111
χ15111111111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-11111-1-11-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-11111-1-11-1-1-1
χ16111111111111-1-1-1-111-1-1-1-1-1-11111-1-11-1-1-111-1-111-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-11111-1-11-1-1-111-1-111-1-1-1111
χ1722222222-2-2-2-2222222-2-20000000000-200-200000000000022222222-2-2-2-2222222-2-20000000000-200-2000000000000
χ1822222222-2-2-2-222-2-2-2-2-2-20000000000200200000000000022222222-2-2-2-222-2-2-2-2-2-200000000002002000000000000
χ1922222222-2-2-2-2-2-222-2-2220000000000200-200000000000022222222-2-2-2-2-2-222-2-2220000000000200-2000000000000
χ2022222222-2-2-2-2-2-2-2-222220000000000-200200000000000022222222-2-2-2-2-2-2-2-222220000000000-2002000000000000
χ2122-22-2-2-2222-2-20000000000002i2i−2i−2i0002i−2i0002-20000000022-22-2-2-2222-2-20000000000002i2i−2i−2i0002i−2i0002-200000000
χ2222-22-2-2-2222-2-20000000000002i2i−2i−2i000−2i2i000-220000000022-22-2-2-2222-2-20000000000002i2i−2i−2i000−2i2i000-2200000000
χ2322-22-2-2-2222-2-2000000000000−2i−2i2i2i0002i−2i000-220000000022-22-2-2-2222-2-2000000000000−2i−2i2i2i0002i−2i000-2200000000
χ2422-22-2-2-2222-2-2000000000000−2i−2i2i2i000−2i2i0002-20000000022-22-2-2-2222-2-2000000000000−2i−2i2i2i000−2i2i0002-200000000
χ2522-2-2-222-200002-22-22-200i2i2−i2−i2i2−i2i2−i20000000000i2−i2i2−i2000022-2-2-222-200002-22-22-200i2i2−i2−i2i2−i2i2−i20000000000i2−i2i2−i20000
χ2622-2-2-222-200002-22-22-200−i2−i2i2i2−i2i2−i2i20000000000−i2i2−i2i2000022-2-2-222-200002-22-22-200−i2−i2i2i2−i2i2−i2i20000000000−i2i2−i2i20000
χ2722-2-2-222-200002-2-22-2200i2i2−i2−i2i2−i2i2−i20000000000−i2i2−i2i2000022-2-2-222-200002-2-22-2200i2i2−i2−i2i2−i2i2−i20000000000−i2i2−i2i20000
χ2822-2-2-222-200002-2-22-2200−i2−i2i2i2−i2i2−i2i20000000000i2−i2i2−i2000022-2-2-222-200002-2-22-2200−i2−i2i2i2−i2i2−i2i20000000000i2−i2i2−i20000
χ2922-2-2-222-20000-222-2-2200i2i2−i2−i2−i2i2−i2i20000000000i2−i2−i2i2000022-2-2-222-20000-222-2-2200i2i2−i2−i2−i2i2−i2i20000000000i2−i2−i2i20000
χ3022-2-2-222-20000-222-2-2200−i2−i2i2i2i2−i2i2−i20000000000−i2i2i2−i2000022-2-2-222-20000-222-2-2200−i2−i2i2i2i2−i2i2−i20000000000−i2i2i2−i20000
χ3122-2-2-222-20000-22-222-200i2i2−i2−i2−i2i2−i2i20000000000−i2i2i2−i2000022-2-2-222-20000-22-222-200i2i2−i2−i2−i2i2−i2i20000000000−i2i2i2−i20000
χ3222-2-2-222-20000-22-222-200−i2−i2i2i2i2−i2i2−i20000000000i2−i2−i2i2000022-2-2-222-20000-22-222-200−i2−i2i2i2i2−i2i2−i20000000000i2−i2−i2i20000
χ332-2-2-22-222-22-22000000002-22-200002-200002-200000000002-2-2-22-222-22-22000000002-22-200002-200002-20000000000
χ342-2-2-22-222-22-22000000002-22-20000-220000-2200000000002-2-2-22-222-22-22000000002-22-20000-220000-220000000000
χ352-2-2-22-222-22-2200000000-22-2200002-20000-2200000000002-2-2-22-222-22-2200000000-22-2200002-20000-220000000000
χ362-2-2-22-222-22-2200000000-22-220000-2200002-200000000002-2-2-22-222-22-2200000000-22-220000-2200002-20000000000
χ37444-44-4-4-4000000000000000022−22−2222000000000000000000444-44-4-4-4000000000000000022−22−2222000000000000000000
χ38444-44-4-4-40000000000000000−222222−22000000000000000000444-44-4-4-40000000000000000−222222−22000000000000000000
χ3944-44-4-4-44-4-444000000000000000000000000000000000044-44-4-4-44-4-4440000000000000000000000000000000000
χ404-444-4-44-40000000000002i2−2i2−2i22i200000000000000000000004-444-4-44-40000000000002i2−2i2−2i22i20000000000000000000000
χ414-444-4-44-4000000000000−2i22i22i2−2i200000000000000000000004-444-4-44-4000000000000−2i22i22i2−2i20000000000000000000000
χ424-44-4-44-444-4-4400000000000000000000000000000000004-44-4-44-444-4-440000000000000000000000000000000000
χ434-44-4-44-44-444-400000000000000000000000000000000004-44-4-44-44-444-40000000000000000000000000000000000
χ444-4-4444-4-400000000004i−4i000000000000000000000000004-4-4444-4-400000000004i−4i00000000000000000000000000
χ454-4-4444-4-40000000000−4i4i000000000000000000000000004-4-4444-4-40000000000−4i4i00000000000000000000000000
χ464-4-4-44-4444-44-400000000000000000000000000000000004-4-4-44-4444-44-40000000000000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ481111111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11111-1-1-1-11111
χ4911111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1
χ5011111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-11111-1-111
χ5111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-11
χ5211111111111111-1-1-1-11111111111-1-1-111-1-1-111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1111-1-111111-11-1
χ5311111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1111111-1-1-1-1-1-11-1-11
χ5411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111-1-11-1-111-1-1-1-1-111-1
χ55111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-11111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111-1-1-1-1-1-1-111111-1
χ56111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111-1-1-11111-1-111-1-1-11
χ57111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1111-1111111-1-1-1-11-1
χ58111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-11111111-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111-1-1-1-1-1-1-111-1-111-11
χ59111111111111-1-1-1-111-1-11111-1-1-1-111111-111-1-1-1-111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-11-111
χ60111111111111-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-1-1-111-1-1111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-111111-1-111-1-1-11-1-1
χ61111111111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1111
χ62111111111111-1-1-1-111-1-1-1-1-1-11111-1-11-1-1-111-1-111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1111-1-111-1-1111-1-1-1
χ6322222222-2-2-2-2222222-2-20000000000-200-2000000000000-2-2-2-2-2-2-2-22222-2-2-2-2-2-22200000000002002000000000000
χ6422222222-2-2-2-222-2-2-2-2-2-200000000002002000000000000-2-2-2-2-2-2-2-22222-2-22222220000000000-200-2000000000000
χ6522222222-2-2-2-2-2-222-2-2220000000000200-2000000000000-2-2-2-2-2-2-2-2222222-2-222-2-20000000000-2002000000000000
χ6622222222-2-2-2-2-2-2-2-222220000000000-2002000000000000-2-2-2-2-2-2-2-222222222-2-2-2-20000000000200-2000000000000
χ6722-22-2-2-2222-2-20000000000002i2i−2i−2i0002i−2i0002-200000000-2-22-2222-2-2-222000000000000−2i−2i2i2i000−2i2i000-2200000000
χ6822-22-2-2-2222-2-20000000000002i2i−2i−2i000−2i2i000-2200000000-2-22-2222-2-2-222000000000000−2i−2i2i2i0002i−2i0002-200000000
χ6922-22-2-2-2222-2-2000000000000−2i−2i2i2i0002i−2i000-2200000000-2-22-2222-2-2-2220000000000002i2i−2i−2i000−2i2i0002-200000000
χ7022-22-2-2-2222-2-2000000000000−2i−2i2i2i000−2i2i0002-200000000-2-22-2222-2-2-2220000000000002i2i−2i−2i0002i−2i000-2200000000
χ7122-2-2-222-200002-22-22-200i2i2−i2−i2i2−i2i2−i20000000000i2−i2i2−i20000-2-2222-2-220000-22-22-2200−i2−i2i2i2−i2i2−i2i20000000000−i2i2−i2i20000
χ7222-2-2-222-200002-22-22-200−i2−i2i2i2−i2i2−i2i20000000000−i2i2−i2i20000-2-2222-2-220000-22-22-2200i2i2−i2−i2i2−i2i2−i20000000000i2−i2i2−i20000
χ7322-2-2-222-200002-2-22-2200i2i2−i2−i2i2−i2i2−i20000000000−i2i2−i2i20000-2-2222-2-220000-222-22-200−i2−i2i2i2−i2i2−i2i20000000000i2−i2i2−i20000
χ7422-2-2-222-200002-2-22-2200−i2−i2i2i2−i2i2−i2i20000000000i2−i2i2−i20000-2-2222-2-220000-222-22-200i2i2−i2−i2i2−i2i2−i20000000000−i2i2−i2i20000
χ7522-2-2-222-20000-222-2-2200i2i2−i2−i2−i2i2−i2i20000000000i2−i2−i2i20000-2-2222-2-2200002-2-222-200−i2−i2i2i2i2−i2i2−i20000000000−i2i2i2−i20000
χ7622-2-2-222-20000-222-2-2200−i2−i2i2i2i2−i2i2−i20000000000−i2i2i2−i20000-2-2222-2-2200002-2-222-200i2i2−i2−i2−i2i2−i2i20000000000i2−i2−i2i20000
χ7722-2-2-222-20000-22-222-200i2i2−i2−i2−i2i2−i2i20000000000−i2i2i2−i20000-2-2222-2-2200002-22-2-2200−i2−i2i2i2i2−i2i2−i20000000000i2−i2−i2i20000
χ7822-2-2-222-20000-22-222-200−i2−i2i2i2i2−i2i2−i20000000000i2−i2−i2i20000-2-2222-2-2200002-22-2-2200i2i2−i2−i2−i2i2−i2i20000000000−i2i2i2−i20000
χ792-2-2-22-222-22-22000000002-22-200002-200002-20000000000-2222-22-2-22-22-200000000-22-220000-220000-220000000000
χ802-2-2-22-222-22-22000000002-22-20000-220000-220000000000-2222-22-2-22-22-200000000-22-2200002-200002-20000000000
χ812-2-2-22-222-22-2200000000-22-2200002-20000-220000000000-2222-22-2-22-22-2000000002-22-20000-2200002-20000000000
χ822-2-2-22-222-22-2200000000-22-220000-2200002-20000000000-2222-22-2-22-22-2000000002-22-200002-20000-220000000000
χ83444-44-4-4-4000000000000000022−22−2222000000000000000000-4-4-44-44440000000000000000−222222−22000000000000000000
χ84444-44-4-4-40000000000000000−222222−22000000000000000000-4-4-44-4444000000000000000022−22−2222000000000000000000
χ8544-44-4-4-44-4-4440000000000000000000000000000000000-4-44-4444-444-4-40000000000000000000000000000000000
χ864-444-4-44-40000000000002i2−2i2−2i22i20000000000000000000000-44-4-444-44000000000000−2i22i22i2−2i20000000000000000000000
χ874-444-4-44-4000000000000−2i22i22i2−2i20000000000000000000000-44-4-444-440000000000002i2−2i2−2i22i20000000000000000000000
χ884-44-4-44-444-4-440000000000000000000000000000000000-44-444-44-4-444-40000000000000000000000000000000000
χ894-44-4-44-44-444-40000000000000000000000000000000000-44-444-44-44-4-440000000000000000000000000000000000
χ904-4-4444-4-400000000004i−4i00000000000000000000000000-444-4-4-4440000000000−4i4i00000000000000000000000000
χ914-4-4444-4-40000000000−4i4i00000000000000000000000000-444-4-4-44400000000004i−4i00000000000000000000000000
χ924-4-4-44-4444-44-40000000000000000000000000000000000-4444-44-4-4-44-440000000000000000000000000000000000

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