Finite Group Databasebeta

← Group #295892

Character table — Group #295892

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444224444444444488888888888888888888888824444444
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
χ31111111111111111111111111111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1
χ41111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111
χ511111111111111111111111111-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111
χ611111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-111-1-1-1-1-1
χ711111111111111111111111111-1-1-1-11-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ811111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91111111111-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11111-1
χ101111111111-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1111-11
χ111111111111-1-1-1-11111111-1-1-1-1111-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-11
χ121111111111-1-1-1-11111111-1-1-1-1111-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ131111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1
χ141111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-11
χ151111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-111-11
χ161111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1111-1
χ1722222222222222-2-222-2-2-222-2-2-22200-200000022000000000000000000000000-200-20000
χ1822222222222222-2-222-2-2-222-2-2-2-2-200-2000000-2-200000000000000000000000020020000
χ192222222222-2-2-2-2-2-222-2-2-2-2-222-222002000000-2-2000000000000000000000000200-20000
χ202222222222-2-2-2-2-2-222-2-2-2-2-222-2-2-200200000022000000000000000000000000-20020000
χ2122222222-2-2222222-2-222-2-2-222-20022-2220000000000000000000000000000000-2-200000
χ2222222222-2-2222222-2-222-2-2-222-200-2-2-2-2-200000000000000000000000000000002200000
χ2322222222-2-22222-2-2-2-2-2-22-2-2-2-22000020022-2-20000000000000000000000000000002-200
χ2422222222-2-22222-2-2-2-2-2-22-2-2-2-220000200-2-222000000000000000000000000000000-2200
χ2522222222-2-2-2-2-2-222-2-222-222-2-2-200222-2-20000000000000000000000000000000-2200000
χ2622222222-2-2-2-2-2-222-2-222-222-2-2-200-2-222200000000000000000000000000000002-200000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-20022-2-2000000000000000000000000000000-2200
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-200-2-2220000000000000000000000000000002-200
χ29222-2-2-2-222-200002-22-22-2-20000200000002i−2i2i−2i00000022-2-22i2i−2i−2i00000000000000000000
χ30222-2-2-2-222-200002-22-22-2-20000200000002i−2i2i−2i000000-2-222−2i−2i2i2i00000000000000000000
χ31222-2-2-2-222-200002-22-22-2-2000020000000−2i2i−2i2i00000022-2-2−2i−2i2i2i00000000000000000000
χ32222-2-2-2-222-200002-22-22-2-2000020000000−2i2i−2i2i000000-2-2222i2i−2i−2i00000000000000000000
χ33222-2-2-2-22-220000-22-22-22-20000200000002i−2i−2i2i0022-2-2000000002i2i−2i−2i0000000000000000
χ34222-2-2-2-22-220000-22-22-22-20000200000002i−2i−2i2i00-2-22200000000−2i−2i2i2i0000000000000000
χ35222-2-2-2-22-220000-22-22-22-2000020000000−2i2i2i−2i0022-2-200000000−2i−2i2i2i0000000000000000
χ36222-2-2-2-22-220000-22-22-22-2000020000000−2i2i2i−2i00-2-222000000002i2i−2i−2i0000000000000000
χ3722-2-222-2-22-22i2i−2i−2i00-220002i−2i0002-20000000002i−2ii2−i2i2−i22−22−200000000i2i2−i2−i222−2−200000000
χ3822-2-222-2-22-22i2i−2i−2i00-220002i−2i0002-20000000002i−2i−i2i2−i2i2−22−2200000000−i2−i2i2i2−2−22200000000
χ3922-2-222-2-22-22i2i−2i−2i00-220002i−2i000-22000000000−2i2ii2−i2i2−i22−22−200000000−i2−i2i2i2−2−22200000000
χ4022-2-222-2-22-22i2i−2i−2i00-220002i−2i000-22000000000−2i2i−i2i2−i2i2−22−2200000000i2i2−i2−i222−2−200000000
χ4122-2-222-2-22-2−2i−2i2i2i00-22000−2i2i0002-2000000000−2i2ii2−i2i2−i2−22−2200000000i2i2−i2−i2−2−22200000000
χ4222-2-222-2-22-2−2i−2i2i2i00-22000−2i2i0002-2000000000−2i2i−i2i2−i2i22−22−200000000−i2−i2i2i222−2−200000000
χ4322-2-222-2-22-2−2i−2i2i2i00-22000−2i2i000-220000000002i−2ii2−i2i2−i2−22−2200000000−i2−i2i2i222−2−200000000
χ4422-2-222-2-22-2−2i−2i2i2i00-22000−2i2i000-220000000002i−2i−i2i2−i2i22−22−200000000i2i2−i2−i2−2−22200000000
χ452-2-222-2-22002-22-22200-2-20002-20002-202-200000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ462-2-222-2-22002-22-22200-2-20002-20002-202-200000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ472-2-222-2-22002-22-22200-2-20002-2000-220-2200000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ482-2-222-2-22002-22-22200-2-20002-2000-220-2200000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ492-2-222-2-2200-22-222200-2-2000-220002-20-2200000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ502-2-222-2-2200-22-222200-2-2000-220002-20-2200000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ512-2-222-2-2200-22-222200-2-2000-22000-2202-200000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ522-2-222-2-2200-22-222200-2-2000-22000-2202-200000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ53444-4-4-4-444-40000-444-4-4440000-4000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4400004-4-444-440000-4000000000000000000000000000000000000000000000
χ5544-44-4-44-444000000-4-4000000000000000000000000022−22−2222000000000000000000000000
χ5644-44-4-44-444000000-4-40000000000000000000000000−222222−22000000000000000000000000
χ5744-44-4-44-4-4-4000000440000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ5844-44-4-44-4-4-400000044000000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ5944-4-444-4-4-444i4i−4i−4i004-4000−4i4i000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-44−4i−4i4i4i004-40004i−4i000000000000000000000000000000000000000000000000
χ614-44-44-44-4004i−4i−4i4i000000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ624-44-44-44-4004i−4i−4i4i00000000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ634-44-44-44-400−4i4i4i−4i000000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ644-44-44-44-400−4i4i4i−4i00000000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ654-4-444-4-44004-44-4-4-40044000-440000000000000000000000000000000000000000000000
χ664-4-444-4-4400-44-44-4-400440004-40000000000000000000000000000000000000000000000
χ674-4-4-4-44440000004-400-4400000000000000000000000000022−22−222200000000000000000000
χ684-4-4-4-44440000004-400-44000000000000000000000000000−222222−2200000000000000000000
χ694-4-4-4-4444000000-44004-4000000000000000000000000000000022−22−22220000000000000000
χ704-4-4-4-4444000000-44004-40000000000000000000000000000000−222222−220000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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