Finite Group Databasebeta

← Group #258564

Character table — Group #258564

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ511111111111111111111111-1-1-1-11-1-1111-1-1-1-11111111111-1-11-1-11-1-1-1-11111-1-1-1-1
χ611111111111111111111111-1-1-1-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11111
χ711111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111111111-111-11111-1-1-1-1-1-1-1-1
χ811111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111111
χ91111111111111111-1-1-1-11-1-111111-1-111-111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-111-1-1
χ101111111111111111-1-1-1-11-1-111111-1-111-111-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-111-1-111
χ111111111111111111-1-1-1-11-1-111111-1-1-1-1-111-1-1111111-1-1-1-1-1-1111-1-1-111-1-11111-1-1
χ121111111111111111-1-1-1-11-1-111111-1-1-1-1-111-1-111-1-1-1-1111111111-1-1-1-1-111-1-1-1-111
χ131111111111111111-1-1-1-11-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-1-1111-1-11111-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-1-1-111111-1-1-111-1-1-1-1-1-1111111-1111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-1-111-1-111
χ161111111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-11111-1-11-1-1-1111111-1-111-1-1
χ172222222222-2-2-222-222-2-2-2222222-22200-2-2-2-2-20000000000000000000000000000
χ182222222222-2-2-222-222-2-2-222-2-2-2-2-2-2-200-222220000000000000000000000000000
χ192222222222-2-2-222-2-2-222-2-2-22222-2-2-2002-2-2220000000000000000000000000000
χ202222222222-2-2-222-2-2-222-2-2-2-2-2-2-2-22200222-2-20000000000000000000000000000
χ2122222222-2-2222-2-222222-2-2-20000-20022-20000220000000000-200-2000000000000
χ2222222222-2-2222-2-222222-2-2-20000-200-2-2-20000-2-200000000002002000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2220000-2002220000-2-20000000000200-2000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2220000-200-2-220000220000000000-2002000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22-2-20000200002000000000000000002-202-20000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22-2-2000020000200000000000000000-220-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222000020000-2000000000000000002-20-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222000020000-200000000000000000-2202-20000000000
χ29222-2-22-2-2-2-20002202-20002-222-2-202-2000000000i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2
χ30222-2-22-2-2-2-20002202-20002-222-2-202-2000000000−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2
χ31222-2-22-2-2-2-20002202-20002-2-2-2220-22000000000i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2
χ32222-2-22-2-2-2-20002202-20002-2-2-2220-22000000000−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2
χ33222-2-22-2-2-2-2000220-22000-2222-2-20-22000000000i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i2
χ34222-2-22-2-2-2-2000220-22000-2222-2-20-22000000000−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i2
χ35222-2-22-2-2-2-2000220-22000-22-2-22202-2000000000i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i2
χ36222-2-22-2-2-2-2000220-22000-22-2-22202-2000000000−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i2
χ372-222-2-22-22-222-22-2-20000-2002i−2i2i−2i2000002i−2i000000000000000000002i−2i002-20000
χ382-222-2-22-22-222-22-2-20000-2002i−2i2i−2i2000002i−2i00000000000000000000−2i2i00-220000
χ392-222-2-22-22-222-22-2-20000-200−2i2i−2i2i200000−2i2i000000000000000000002i−2i00-220000
χ402-222-2-22-22-222-22-2-20000-200−2i2i−2i2i200000−2i2i00000000000000000000−2i2i002-20000
χ412-222-2-22-22-2-2-222-2200002002i−2i2i−2i-200000−2i2i0000000000002-2000000002i−2i000000
χ422-222-2-22-22-2-2-222-2200002002i−2i2i−2i-200000−2i2i000000000000-2200000000−2i2i000000
χ432-222-2-22-22-2-2-222-220000200−2i2i−2i2i-2000002i−2i0000000000002-200000000−2i2i000000
χ442-222-2-22-22-2-2-222-220000200−2i2i−2i2i-2000002i−2i000000000000-22000000002i−2i000000
χ45444-4-44-4-444000-4-404-4000-44000000000000000000000000000000000000000000
χ46444-4-44-4-444000-4-40-440004-4000000000000000000000000000000000000000000
χ4744-444-4-4-4004-4400-400000000000000000000000000022−2222−22000000000000000000
χ4844-444-4-4-4004-4400-4000000000000000000000000000−2222−2222000000000000000000
χ4944-444-4-4-400-44-4004000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ5044-444-4-4-400-44-400400000000000000000000000−2i22i2−2i22i20000000000000000000000
χ5144-4-4-4-44400000000004i−4i00000000000000000002-2-222i−2i−2i2i000000000000000000
χ5244-4-4-4-44400000000004i−4i0000000000000000000-222-2−2i2i2i−2i000000000000000000
χ5344-4-4-4-4440000000000−4i4i00000000000000000002-2-22−2i2i2i−2i000000000000000000
χ5444-4-4-4-4440000000000−4i4i0000000000000000000-222-22i−2i−2i2i000000000000000000
χ554-444-4-44-4-4444-4-44-400004000000-40000000000000000000000000000000000000
χ564-444-4-44-4-44-4-44-4440000-400000040000000000000000000000000000000000000
χ574-44-44-4-444-4000-44000000000000000000004i−4i0000000000000000000000000000
χ584-44-44-4-444-4000-4400000000000000000000−4i4i0000000000000000000000000000
χ594-44-44-4-44-440004-4000000004i−4i−4i4i00000000000000000000000000000000000000
χ604-44-44-4-44-440004-400000000−4i4i4i−4i00000000000000000000000000000000000000
χ614-4-44-44-44004-4-4004000000000000004-4000000000000000000000000000000000
χ624-4-44-44-44004-4-400400000000000000-44000000000000000000000000000000000
χ634-4-44-44-4400-44400-40000000000000000000004i−4i00000000000000000000000000
χ644-4-44-44-4400-44400-4000000000000000000000−4i4i00000000000000000000000000
χ658-8-8-8888-8000000000000000000000000000000000000000000000000000000000

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