Finite Group Databasebeta

← Group #257947

Character table — Group #257947

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444442244444422444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1111-1-1-1-1
χ3111111111111111111111111111-1-111-1-111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-11111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-1-11-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-11111-111-1-1-1-1
χ91111111111111111-1-1-1-1-1-11111-111-1-1111111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-111-111-1-111
χ111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-111111-1-1-1-111
χ121111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-1-11-1-111-1-1
χ131111111111111111-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-11-1-11111111-1-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1111-1-111
χ1722222222222-2-2-2-222222-2-2-2-200-22200-2-200000000000000000-200000002000000
χ1822222222222-2-2-2-222222-2-2-2-200-2-2-200220000000000000000020000000-2000000
χ1922222222222-2-2-2-22-2-2-2-222-2-20022200-2-20000000000000000020000000-2000000
χ2022222222222-2-2-2-22-2-2-2-222-2-2002-2-2002200000000000000000-200000002000000
χ2122222222-2-2-22222-222-2-222-2-222-20022000000000000000000-2000-200000000000
χ2222222222-2-2-22222-222-2-222-2-2-2-2-200-2-20000000000000000002000200000000000
χ2322222222-2-2-22222-2-2-222-2-2-2-222200-2-2000000000000000000-2000200000000000
χ2422222222-2-2-22222-2-2-222-2-2-2-2-2-2200220000000000000000002000-200000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2220020000000000000000000000000002-20002-20000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222002000000000000000000000000000-22000-220000
χ2722222222-2-2-2-2-2-2-2-2-2-222222200-20000000000000000000000000002-2000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200-2000000000000000000000000000-220002-20000
χ29222-2-22-2-22-2-22-22-220000002-20002i−2i002i−2i000022-2-20000000000000002i−2i0000000
χ30222-2-22-2-22-2-22-22-220000002-20002i−2i002i−2i0000-2-222000000000000000−2i2i0000000
χ31222-2-22-2-22-2-22-22-220000002-2000−2i2i00−2i2i000022-2-2000000000000000−2i2i0000000
χ32222-2-22-2-22-2-22-22-220000002-2000−2i2i00−2i2i0000-2-2220000000000000002i−2i0000000
χ33222-2-22-2-22-2-2-22-222000000-220002i−2i00−2i2i22-2-2000000000000002i−2i000000000000
χ34222-2-22-2-22-2-2-22-222000000-220002i−2i00−2i2i-2-22200000000000000−2i2i000000000000
χ35222-2-22-2-22-2-2-22-222000000-22000−2i2i002i−2i22-2-200000000000000−2i2i000000000000
χ36222-2-22-2-22-2-2-22-222000000-22000−2i2i002i−2i-2-222000000000000002i−2i000000000000
χ372-2-22-22-2200022-2-202-2002-2002-20002-200i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ382-2-22-22-2200022-2-202-2002-2002-20002-200−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ392-2-22-22-2200022-2-202-2002-200-22000-2200i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ402-2-22-22-2200022-2-202-2002-200-22000-2200−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ412-2-22-22-2200022-2-20-2200-22002-2000-2200i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ422-2-22-22-2200022-2-20-2200-22002-2000-2200−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ432-2-22-22-2200022-2-20-2200-2200-220002-200i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ442-2-22-22-2200022-2-20-2200-2200-220002-200−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ45444-4-44-4-4-4444-44-4-4000000-4400000000000000000000000000000000000000000
χ46444-4-44-4-4-444-44-44-40000004-400000000000000000000000000000000000000000
χ4744-4-44-4-4400000000004i−4i0000000000000000000002-22-22i−2i2i−2i0000000000000000
χ4844-4-44-4-4400000000004i−4i000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ4944-4-44-4-440000000000−4i4i0000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ5044-4-44-4-440000000000−4i4i000000000000000000000-22-222i−2i2i−2i0000000000000000
χ514-4444-4-4-444-40000-400000000000000000000000000000000000000000000022−2200
χ524-4444-4-4-444-40000-4000000000000000000000000000000000000000000000−222200
χ534-4444-4-4-4-4-4400004000000000000000000000000000000000000000000000002i2−2i2
χ544-4444-4-4-4-4-440000400000000000000000000000000000000000000000000000−2i22i2
χ554-44-4-4-4444-440000-400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ564-44-4-4-4444-440000-40000000000000000000000000−2i22i22i2−2i200000000000000000000
χ574-44-4-4-444-44-4000040000000000000000000000000000022−22−22220000000000000000
χ584-44-4-4-444-44-40000400000000000000000000000000000−222222−220000000000000000
χ594-4-44-44-44000-4-44404-400-440000000000000000000000000000000000000000000
χ604-4-44-44-44000-4-4440-44004-40000000000000000000000000000000000000000000
χ614-4-4-4444-40004-4-4400000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-4-4444-40004-4-440000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ634-4-4-4444-4000-444-40000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ644-4-4-4444-4000-444-4000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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