Finite Group Databasebeta

← Group #291050

Character table — Group #291050

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444444444444444488888888888888888888888824444424
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ5111111111111111111111111111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-11-1-11-1-1-1
χ6111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-11-111
χ7111111111111111111111111111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111
χ8111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1
χ91111111111111-1-1-1-1111-1-1-1-111-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1
χ101111111111111-1-1-1-1111-1-1-1-111-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-11
χ111111111111111-1-1-1-1111-1-1-1-111-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ121111111111111-1-1-1-1111-1-1-1-111-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11-1
χ131111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1111-1-11
χ141111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1111-11-1
χ151111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-111-1
χ161111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111-11-11
χ172222222222-2-2-2222222-2-2-222-2-2-2000000220022000000000000000000000000-20000-200
χ182222222222-2-2-2222222-2-2-222-2-2-2000000-2-200-2-200000000000000000000000020000200
χ192222222222-2-2-2-2-2-2-222-222-2-2-2-220000002200-2-200000000000000000000000020000-200
χ202222222222-2-2-2-2-2-2-222-222-2-2-2-22000000-2-20022000000000000000000000000-20000200
χ2122222222-2-22222222-2-2222-2-2-2-2-20000220022000000000000000000000000000-200-2000
χ2222222222-2-22222222-2-2222-2-2-2-2-20000-2-200-2-20000000000000000000000000002002000
χ2322222222-2-2222-2-2-2-2-2-22-2-222-2-2200002200-2-2000000000000000000000000000200-2000
χ2422222222-2-2222-2-2-2-2-2-22-2-222-2-220000-2-20022000000000000000000000000000-2002000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-222222-2-200000000000000000000000000000000002-20000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-2222-2-2220000000000000000000000000000000000-220000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-222-2-20000000000000000000000000000000000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-22200000000000000000000000000000000002-20000
χ29222-2-22-2-2222-2-20000-2-2200002-202i−2i2i−2i000000002i2i−2i−2i000022-2-200000000000000000000
χ30222-2-22-2-2222-2-20000-2-2200002-202i−2i2i−2i00000000−2i−2i2i2i0000-2-22200000000000000000000
χ31222-2-22-2-2222-2-20000-2-2200002-20−2i2i−2i2i000000002i2i−2i−2i0000-2-22200000000000000000000
χ32222-2-22-2-2222-2-20000-2-2200002-20−2i2i−2i2i00000000−2i−2i2i2i000022-2-200000000000000000000
χ33222-2-22-2-2-2-2-222000022-200002-202i−2i−2i2i00000000000022-2-200002i2i−2i−2i0000000000000000
χ34222-2-22-2-2-2-2-222000022-200002-202i−2i−2i2i000000000000-2-2220000−2i−2i2i2i0000000000000000
χ35222-2-22-2-2-2-2-222000022-200002-20−2i2i2i−2i00000000000022-2-20000−2i−2i2i2i0000000000000000
χ36222-2-22-2-2-2-2-222000022-200002-20−2i2i2i−2i000000000000-2-22200002i2i−2i−2i0000000000000000
χ3722-22-2-22-22-20002i2i−2i−2i2-20002i−2i0000000002-2002i−2i00000000i2−i2i2−i22−22−2i2i2−i2−i222−2−200000000
χ3822-22-2-22-22-20002i2i−2i−2i2-20002i−2i0000000002-2002i−2i00000000−i2i2−i2i2−22−22−i2−i2i2i2−2−22200000000
χ3922-22-2-22-22-20002i2i−2i−2i2-20002i−2i000000000-2200−2i2i00000000i2−i2i2−i22−22−2−i2−i2i2i2−2−22200000000
χ4022-22-2-22-22-20002i2i−2i−2i2-20002i−2i000000000-2200−2i2i00000000−i2i2−i2i2−22−22i2i2−i2−i222−2−200000000
χ4122-22-2-22-22-2000−2i−2i2i2i2-2000−2i2i0000000002-200−2i2i00000000i2−i2i2−i2−22−22i2i2−i2−i2−2−22200000000
χ4222-22-2-22-22-2000−2i−2i2i2i2-2000−2i2i0000000002-200−2i2i00000000−i2i2−i2i22−22−2−i2−i2i2i222−2−200000000
χ4322-22-2-22-22-2000−2i−2i2i2i2-2000−2i2i000000000-22002i−2i00000000i2−i2i2−i2−22−22−i2−i2i2i222−2−200000000
χ4422-22-2-22-22-2000−2i−2i2i2i2-2000−2i2i000000000-22002i−2i00000000−i2i2−i2i22−22−2i2i2−i2−i2−2−22200000000
χ452-2-22-22-220022-22-22-200-22-20000000002i−2i002i−2i002−22−22−22−200000000i2−i2i2−i2i2−i2i2−i200000000
χ462-2-22-22-220022-22-22-200-22-20000000002i−2i002i−2i00−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i200000000
χ472-2-22-22-220022-22-22-200-22-2000000000−2i2i00−2i2i002−22−22−22−200000000−i2i2−i2i2−i2i2−i2i200000000
χ482-2-22-22-220022-22-22-200-22-2000000000−2i2i00−2i2i00−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i200000000
χ492-2-22-22-220022-2-22-2200-2-220000000002i−2i00−2i2i002−22−2−22−2200000000i2−i2i2−i2−i2i2−i2i200000000
χ502-2-22-22-220022-2-22-2200-2-220000000002i−2i00−2i2i00−22−222−22−200000000−i2i2−i2i2i2−i2i2−i200000000
χ512-2-22-22-220022-2-22-2200-2-22000000000−2i2i002i−2i002−22−2−22−2200000000−i2i2−i2i2i2−i2i2−i200000000
χ522-2-22-22-220022-2-22-2200-2-22000000000−2i2i002i−2i00−22−222−22−200000000i2−i2i2−i2−i2i2−i2i200000000
χ53444-4-44-4-444-4440000-4-4-40000-44000000000000000000000000000000000000000000000
χ54444-4-44-4-4-4-44-4-400004440000-44000000000000000000000000000000000000000000000
χ5544-44-4-44-4-440004i4i−4i−4i-44000−4i4i00000000000000000000000000000000000000000000000
χ5644-44-4-44-4-44000−4i−4i4i4i-440004i−4i00000000000000000000000000000000000000000000000
χ5744-4-44-4-444-40000000-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ5844-4-44-4-444-40000000-440000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ5944-4-44-4-44-4400000004-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ6044-4-44-4-44-4400000004-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ614-4444-4-4-4000004i−4i−4i4i000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ624-4444-4-4-4000004i−4i−4i4i00000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ634-4444-4-4-400000−4i4i4i−4i000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ644-4444-4-4-400000−4i4i4i−4i00000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ654-4-44-44-4400-4-444-44-4004-440000000000000000000000000000000000000000000000000
χ664-4-44-44-4400-4-44-44-440044-40000000000000000000000000000000000000000000000000
χ674-4-4-4444-4004-44000000-400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ684-4-4-4444-4004-44000000-40000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ694-4-4-4444-400-44-400000040000000000000000000000022−22−2222000000000000000000000000
χ704-4-4-4444-400-44-4000000400000000000000000000000−222222−22000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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