Finite Group Databasebeta

← Group #247253

Character table — Group #247253

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444442244444444442244444444488888888222244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111-1-1111-1-111-1-111111111-1-1-1-11-1-11-1-1-1-1-1-11111
χ611111111111111111111-1-1-1-11111-1-1111-1-111-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-1
χ711111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1111111111111-111-111-1-1-1-1-1-1-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111
χ91111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1111111-1-1-1-111-1-1111-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-111-1-1-1-11111-1-111111-1-1-1-1-111-1-111
χ111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111111-1-1-1-111
χ121111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1111111-1-11-1-1-11111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-11111-1-1-1-111-1-1-1111-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-11111-1-111-1111-1-111-1-111-1-1
χ1722222222222-2-2-2-2222222222-2-2-2-22200-2-2-200-2-200000000000000000000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-200-222002200000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2222222-2-2-2-20022200-2-200000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-222-2-222002-2-2002200000000000000000000000000
χ2122222222-2-2-22222-222-2-20000-2-2-2-20022200-2-200000000000000-20020000000000
χ2222222222-2-2-22222-222-2-20000-2-2-2-200-2-22002200000000000000200-20000000000
χ2322222222-2-2-22222-2-2-222000022-2-20022-2002200000000000000-200-20000000000
χ2422222222-2-2-22222-2-2-222000022-2-200-2-2-200-2-20000000000000020020000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2000022220000-200000000000000000002-202-200000000
χ2622222222-2-2-2-2-2-2-2-222-2-2000022220000-20000000000000000000-220-2200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2220000-2-2220000200000000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2220000-2-222000020000000000000000000-2202-200000000
χ29222-22-2-2-22-2-2000022-22-222-2-200002-2000000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i20000
χ30222-22-2-2-22-2-2000022-22-222-2-200002-2000000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i20000
χ31222-22-2-2-22-2-2000022-22-2-2-2220000-22000000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i20000
χ32222-22-2-2-22-2-2000022-22-2-2-2220000-22000000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i20000
χ33222-22-2-2-22-2-200002-22-2222-2-20000-22000000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i20000
χ34222-22-2-2-22-2-200002-22-2222-2-20000-22000000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i20000
χ35222-22-2-2-22-2-200002-22-22-2-22200002-2000000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i20000
χ36222-22-2-2-22-2-200002-22-22-2-22200002-2000000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i20000
χ372-2-2-222-22-22-22-22-2200002-22-2002-20000000002-200000000002-20000000000002-2
χ382-2-2-222-22-22-22-22-2200002-22-2002-20000000002-20000000000-22000000000000-22
χ392-2-2-222-22-22-22-22-220000-22-22002-2000000000-2200000000002-2000000000000-22
χ402-2-2-222-22-22-22-22-220000-22-22002-2000000000-220000000000-220000000000002-2
χ412-2-2-222-22-22-2-22-22200002-22-200-22000000000-22000000002-20000000000002-200
χ422-2-2-222-22-22-2-22-22200002-22-200-22000000000-2200000000-22000000000000-2200
χ432-2-2-222-22-22-2-22-2220000-22-2200-220000000002-2000000002-2000000000000-2200
χ442-2-2-222-22-22-2-22-2220000-22-2200-220000000002-200000000-220000000000002-200
χ45444-44-4-4-4-4440000-44-4-44000000000000000000000000000000000000000000000
χ46444-44-4-4-4-4440000-4-444-4000000000000000000000000000000000000000000000
χ4744-44-44-4-40004-4-4400000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ4844-44-44-4-40004-4-440000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ4944-44-44-4-4000-444-40000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ5044-44-44-4-4000-444-4000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ5144-4-4-4-44400000000000000004-400000000000002-2-222-2-22000000000000000000
χ5244-4-4-4-44400000000000000004-40000000000000-222-2-222-2000000000000000000
χ5344-4-4-4-4440000000000000000-4400000000000002-2-22-222-2000000000000000000
χ5444-4-4-4-4440000000000000000-440000000000000-222-22-2-22000000000000000000
χ554-44-4-444-400044-4-40000000000000004i−4i000000000000000000000000000000000
χ564-44-4-444-400044-4-4000000000000000−4i4i000000000000000000000000000000000
χ574-44-4-444-4000-4-444000000000000000000004-40000000000000000000000000000
χ584-44-4-444-4000-4-44400000000000000000000-440000000000000000000000000000
χ594-4-444-44-444-40000-4000000000000000004i−4i000000000000000000000000000000
χ604-4-444-44-444-40000-400000000000000000−4i4i000000000000000000000000000000
χ614-4-444-44-4-4-440000400004-4-4400000000000000000000000000000000000000000
χ624-4-444-44-4-4-44000040000-444-400000000000000000000000000000000000000000
χ634-4-4-444-444-444-44-4-40000000000-440000000000000000000000000000000000000
χ644-4-4-444-444-44-44-44-400000000004-40000000000000000000000000000000000000
χ658-888-8-8-88000000000000000000000000000000000000000000000000000000000

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