Finite Group Databasebeta

← Group #258313

Character table — Group #258313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422444444444888888888888888824444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111-1-111111-1-1-1-111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111
χ7111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111
χ8111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-111-1-1-1-1
χ91111111111-1-1-1-111111111111-1-1-1-11-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-1-111-1-1
χ101111111111-1-1-1-111111111111-1-1-1-11-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-111-1-111
χ111111111111-1-1-1-111111111111-1-1-1-11-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-111
χ121111111111-1-1-1-111111111111-1-1-1-11-1-1-1-111-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-111111-1-1
χ131111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-1-111-1-111
χ141111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-11111-1-1-111-1-1
χ151111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111-1-111-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-111111-1-1
χ161111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-111-1-1111-1-1-1-111
χ1722222222222222-2-2-222-2-2222222-2-2-2220000-2-2-2-2-2000000000000000000000000000000
χ1822222222222222-2-2-222-2-2-2-2-2-222-2-2-2-2-20000-22222000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-222-2-22222-2-222-2-2-200002-2-222000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2220000222-2-2000000000000000000000000000000
χ2122222222-2-22222222-2-22-20000-2-222-2002222-200000000000000000000-2000000-2000000
χ2222222222-2-22222222-2-22-20000-2-222-200-2-2-2-2-20000000000000000000020000002000000
χ2322222222-2-22222-2-2-2-2-2-220000-2-2-2-2200000020000000000000000000002-22-2000000000
χ2422222222-2-22222-2-2-2-2-2-220000-2-2-2-220000002000000000000000000000-22-22000000000
χ2522222222-2-2-2-2-2-2222-2-22-2000022-2-2-20022-2-2200000000000000000000-20000002000000
χ2622222222-2-2-2-2-2-2222-2-22-2000022-2-2-200-2-2222000000000000000000002000000-2000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22000022222000000-20000000000000000000002-2-22000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22000022222000000-2000000000000000000000-222-2000000000
χ29222-2-2-2-222-2000022-22-2-2-22i2i−2i−2i0000200000002i−2i0022-2-2000000000000000002i−2i0000000
χ30222-2-2-2-222-2000022-22-2-2-22i2i−2i−2i0000200000002i−2i00-2-22200000000000000000−2i2i0000000
χ31222-2-2-2-222-2000022-22-2-2-2−2i−2i2i2i000020000000−2i2i0022-2-200000000000000000−2i2i0000000
χ32222-2-2-2-222-2000022-22-2-2-2−2i−2i2i2i000020000000−2i2i00-2-222000000000000000002i−2i0000000
χ33222-2-2-2-222-20000-2-222-2222i2i−2i−2i0000-20000000−2i2i0000002i2i−2i−2i00000000000000002-20000
χ34222-2-2-2-222-20000-2-222-2222i2i−2i−2i0000-20000000−2i2i000000−2i−2i2i2i0000000000000000-220000
χ35222-2-2-2-222-20000-2-222-222−2i−2i2i2i0000-200000002i−2i0000002i2i−2i−2i0000000000000000-220000
χ36222-2-2-2-222-20000-2-222-222−2i−2i2i2i0000-200000002i−2i000000−2i−2i2i2i00000000000000002-20000
χ3722-2-22-22-22-22i2i−2i−2i000-22002i−2i2i−2i2i−2i0002-200000000000000000i2i2−i2−i222−2−200000000002−2i2−i2
χ3822-2-22-22-22-22i2i−2i−2i000-22002i−2i2i−2i2i−2i0002-200000000000000000−i2−i2i2i2−2−2220000000000−22−i2i2
χ3922-2-22-22-22-22i2i−2i−2i000-2200−2i2i−2i2i2i−2i000-2200000000000000000i2i2−i2−i222−2−20000000000−22−i2i2
χ4022-2-22-22-22-22i2i−2i−2i000-2200−2i2i−2i2i2i−2i000-2200000000000000000−i2−i2i2i2−2−22200000000002−2i2−i2
χ4122-2-22-22-22-2−2i−2i2i2i000-22002i−2i2i−2i−2i2i000-2200000000000000000i2i2−i2−i2−2−22200000000002−2−i2i2
χ4222-2-22-22-22-2−2i−2i2i2i000-22002i−2i2i−2i−2i2i000-2200000000000000000−i2−i2i2i222−2−20000000000−22i2−i2
χ4322-2-22-22-22-2−2i−2i2i2i000-2200−2i2i−2i2i−2i2i0002-200000000000000000i2i2−i2−i2−2−2220000000000−22i2−i2
χ4422-2-22-22-22-2−2i−2i2i2i000-2200−2i2i−2i2i−2i2i0002-200000000000000000−i2−i2i2i222−2−200000000002−2−i2i2
χ452-2-22-2-222002-22-22-2200-200000002-20002i−2i2i−2i000002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000000000
χ462-2-22-2-222002-22-22-2200-200000002-20002i−2i2i−2i00000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000000000
χ472-2-22-2-222002-22-22-2200-200000002-2000−2i2i−2i2i000002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000000000
χ482-2-22-2-222002-22-22-2200-200000002-2000−2i2i−2i2i00000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000000000
χ492-2-22-2-22200-22-222-2200-20000000-220002i−2i−2i2i000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000000000
χ502-2-22-2-22200-22-222-2200-20000000-220002i−2i−2i2i00000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000000000
χ512-2-22-2-22200-22-222-2200-20000000-22000−2i2i2i−2i000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000000000
χ522-2-22-2-22200-22-222-2200-20000000-22000−2i2i2i−2i00000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000
χ53444-4-4-4-44-44000044-4-44-4400000000-400000000000000000000000000000000000000000
χ54444-4-4-4-44-440000-4-44-444-400000000400000000000000000000000000000000000000000
χ5544-44-44-4-4440000000-4-4004-4-440000000000000000000000000000000000000000000000
χ5644-44-44-4-4440000000-4-400-444-40000000000000000000000000000000000000000000000
χ5744-44-44-4-4-4-4000000044000000000000000000004i−4i000000000000000000000000000000
χ5844-44-44-4-4-4-400000004400000000000000000000−4i4i000000000000000000000000000000
χ5944-4-44-44-4-444i4i−4i−4i0004-4000000−4i4i00000000000000000000000000000000000000000000
χ6044-4-44-44-4-44−4i−4i4i4i0004-40000004i−4i00000000000000000000000000000000000000000000
χ614-44-4-444-4004i−4i−4i4i000000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ624-44-4-444-4004i−4i−4i4i00000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ634-44-4-444-400−4i4i4i−4i000000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ644-44-4-444-400−4i4i4i−4i00000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ654-4-44-4-444004-44-4-44-40040000000-44000000000000000000000000000000000000000000
χ664-4-44-4-44400-44-44-44-400400000004-4000000000000000000000000000000000000000000
χ674-4-4-444-440000004-4-400400000000000000000000022−22−222200000000000000000000000000
χ684-4-4-444-440000004-4-4004000000000000000000000−222222−2200000000000000000000000000
χ694-4-4-444-44000000-44400-400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ704-4-4-444-44000000-44400-40000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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