Finite Group Databasebeta

← Group #244849

Character table — Group #244849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222222244888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-111-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-111111111-1-11-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11-11111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-200002222-2-20000222200-2-2002200-2-2000000000000000-2000000000
χ18222222222-22-22-22-200002222-2-20000-2-2-2-200-2-200-2-200220000000000000002000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-200002222002200-2-200-2-20000000000000002000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-2002200220022000000000000000-2000000000
χ2122222222-22-22-22-2222220000-2-222220000-2-2002200-2-20000000000000000-20000000000
χ2222222222-22-22-22-2222220000-2-2-2-2-2-20000-2-200-2-20022000000000000000020000000000
χ2322222222-22-22-22-22-2-2-2-20000-2-2222200002200-2-200-2-2000000000000000020000000000
χ2422222222-22-22-22-22-2-2-2-20000-2-2-2-2-2-2000022002200220000000000000000-20000000000
χ25222-2-2-22-2020-20-20222-2-200000022-2-2i2i2−i2−i200002-20000i2−i20000i2i2−i2−i2i2i2−i2−i200000000i2−i2000
χ26222-2-2-22-2020-20-20222-2-200000022-2-2−i2−i2i2i200002-20000−i2i20000−i2−i2i2i2−i2−i2i2i200000000−i2i2000
χ27222-2-2-22-2020-20-20222-2-2000000-2-222i2i2−i2−i20000-220000i2−i20000i2i2−i2−i2−i2−i2i2i200000000−i2i2000
χ28222-2-2-22-2020-20-20222-2-2000000-2-222−i2−i2i2i20000-220000−i2i20000−i2−i2i2i2i2i2−i2−i200000000i2−i2000
χ29222-2-2-22-2020-20-202-2-22200000022-2-2i2i2−i2−i20000-220000i2−i20000−i2−i2i2i2i2i2−i2−i200000000−i2i2000
χ30222-2-2-22-2020-20-202-2-22200000022-2-2−i2−i2i2i20000-220000−i2i20000i2i2−i2−i2−i2−i2i2i200000000i2−i2000
χ31222-2-2-22-2020-20-202-2-222000000-2-222i2i2−i2−i200002-20000i2−i20000−i2−i2i2i2−i2−i2i2i200000000i2−i2000
χ32222-2-2-22-2020-20-202-2-222000000-2-222−i2−i2i2i200002-20000−i2i20000i2i2−i2−i2i2i2−i2−i200000000−i2i2000
χ3322-22-2-2-2220-20-2020000022-2-200i2−i2i2−i22-22-20000002-2i2−i200i2i2−i2−i20000i2−i2i2−i20000000000i2−i20
χ3422-22-2-2-2220-20-2020000022-2-200i2−i2i2−i2-22-22000000-22i2−i200i2i2−i2−i20000−i2i2−i2i20000000000−i2i20
χ3522-22-2-2-2220-20-2020000022-2-200−i2i2−i2i22-22-20000002-2−i2i200−i2−i2i2i20000−i2i2−i2i20000000000−i2i20
χ3622-22-2-2-2220-20-2020000022-2-200−i2i2−i2i2-22-22000000-22−i2i200−i2−i2i2i20000i2−i2i2−i20000000000i2−i20
χ3722-22-2-2-2220-20-20200000-2-22200i2−i2i2−i22-22-2000000-22i2−i200−i2−i2i2i20000i2−i2i2−i20000000000−i2i20
χ3822-22-2-2-2220-20-20200000-2-22200i2−i2i2−i2-22-220000002-2i2−i200−i2−i2i2i20000−i2i2−i2i20000000000i2−i20
χ3922-22-2-2-2220-20-20200000-2-22200−i2i2−i2i22-22-2000000-22−i2i200i2i2−i2−i20000−i2i2−i2i20000000000i2−i20
χ4022-22-2-2-2220-20-20200000-2-22200−i2i2−i2i2-22-220000002-2−i2i200i2i2−i2−i20000i2−i2i2−i20000000000−i2i20
χ412-2-2-2-22222-2-222-2-222-22-20000-22000000002-200000000002-22-20000000000002-20000000
χ422-2-2-2-22222-2-222-2-222-22-20000-22000000002-20000000000-22-22000000000000-220000000
χ432-2-2-2-22222-2-222-2-22-22-220000-2200000000-2200000000002-22-2000000000000-220000000
χ442-2-2-2-22222-2-222-2-22-22-220000-2200000000-220000000000-22-220000000000002-20000000
χ452-2-2-2-2222-222-2-222-200002-22-2-2200000000002-20000000000002-22-200000000002-200000
χ462-2-2-2-2222-222-2-222-200002-22-2-2200000000002-2000000000000-22-220000000000-2200000
χ472-2-2-2-2222-222-2-222-20000-22-22-220000000000-220000000000002-22-20000000000-2200000
χ482-2-2-2-2222-222-2-222-20000-22-22-220000000000-22000000000000-22-2200000000002-200000
χ492-2-2-2-2222-2-222-2-2222-22-22-22-22-200000000-22-22000000000000000000002-200000000000
χ502-2-2-2-2222-2-222-2-2222-22-2-22-222-200000000-222-200000000000000000000-2200000000000
χ512-2-2-2-2222-2-222-2-222-22-222-22-22-2000000002-2-2200000000000000000000-2200000000000
χ522-2-2-2-2222-2-222-2-222-22-22-22-222-2000000002-22-2000000000000000000002-200000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-40-404040-4000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ55444-4-4-44-40-404040-400000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ5644-44-4-4-44-404040-4000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ5744-44-4-4-44-404040-400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ5844-4-444-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ5944-4-444-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ6044-4-444-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ6144-4-444-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ624-44-44-4-444040-40-400000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ634-44-44-4-444040-40-40000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ644-44-44-4-44-40-40404000004-4-4400000000000000000000000000000000000000000000000
χ654-44-44-4-44-40-4040400000-444-400000000000000000000000000000000000000000000000
χ664-4-444-44-404040-40-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ674-4-444-44-404040-40-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ684-4-444-44-40-40-404044-4-44000000000000000000000000000000000000000000000000000
χ694-4-444-44-40-40-40404-444-4000000000000000000000000000000000000000000000000000
χ704-4-4-4-444444-4-444-4-4000000004-4000000000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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